diff --git a/object/address/address.go b/object/address/address.go
deleted file mode 100644
index 736b034..0000000
--- a/object/address/address.go
+++ /dev/null
@@ -1,192 +0,0 @@
-package address
-
-import (
-	"errors"
-	"fmt"
-	"strings"
-
-	"github.com/nspcc-dev/neofs-api-go/v2/refs"
-	cid "github.com/nspcc-dev/neofs-sdk-go/container/id"
-	oid "github.com/nspcc-dev/neofs-sdk-go/object/id"
-)
-
-// Address represents v2-compatible object address.
-type Address refs.Address
-
-var errInvalidAddressString = errors.New("incorrect format of the string object address")
-
-const (
-	addressParts     = 2
-	addressSeparator = "/"
-)
-
-// NewAddressFromV2 converts v2 Address message to Address.
-//
-// Nil refs.Address converts to nil.
-func NewAddressFromV2(aV2 *refs.Address) *Address {
-	return (*Address)(aV2)
-}
-
-// NewAddress creates and initializes blank Address.
-//
-// Works similar as NewAddressFromV2(new(Address)).
-//
-// Defaults:
-// 	- cid: nil;
-//	- oid: nil.
-func NewAddress() *Address {
-	return NewAddressFromV2(new(refs.Address))
-}
-
-// ToV2 converts Address to v2 Address message.
-//
-// Nil Address converts to nil.
-func (a *Address) ToV2() *refs.Address {
-	return (*refs.Address)(a)
-}
-
-// ContainerID returns container identifier.
-func (a *Address) ContainerID() (v cid.ID, isSet bool) {
-	v2 := (*refs.Address)(a)
-
-	cidV2 := v2.GetContainerID()
-	if cidV2 != nil {
-		_ = v.ReadFromV2(*cidV2)
-		isSet = true
-	}
-
-	return
-}
-
-// SetContainerID sets container identifier.
-func (a *Address) SetContainerID(id cid.ID) {
-	var cidV2 refs.ContainerID
-	id.WriteToV2(&cidV2)
-
-	(*refs.Address)(a).SetContainerID(&cidV2)
-}
-
-// ObjectID returns object identifier.
-func (a *Address) ObjectID() (v oid.ID, isSet bool) {
-	v2 := (*refs.Address)(a)
-
-	oidV2 := v2.GetObjectID()
-	if oidV2 != nil {
-		_ = v.ReadFromV2(*oidV2)
-		isSet = true
-	}
-
-	return
-}
-
-// SetObjectID sets object identifier.
-func (a *Address) SetObjectID(id oid.ID) {
-	var oidV2 refs.ObjectID
-	id.WriteToV2(&oidV2)
-
-	(*refs.Address)(a).SetObjectID(&oidV2)
-}
-
-// Parse converts base58 string representation into Address.
-func (a *Address) Parse(s string) error {
-	var (
-		err   error
-		oid   oid.ID
-		id    cid.ID
-		parts = strings.Split(s, addressSeparator)
-	)
-
-	if len(parts) != addressParts {
-		return errInvalidAddressString
-	} else if err = id.DecodeString(parts[0]); err != nil {
-		return err
-	} else if err = oid.DecodeString(parts[1]); err != nil {
-		return err
-	}
-
-	a.SetObjectID(oid)
-	a.SetContainerID(id)
-
-	return nil
-}
-
-// String returns string representation of Object.Address.
-func (a *Address) String() string {
-	var cidStr, oidStr string
-
-	if cID, set := a.ContainerID(); set {
-		cidStr = cID.String()
-	}
-
-	if oID, set := a.ObjectID(); set {
-		oidStr = oID.String()
-	}
-
-	return strings.Join([]string{cidStr, oidStr}, addressSeparator)
-}
-
-// Marshal marshals Address into a protobuf binary form.
-func (a *Address) Marshal() ([]byte, error) {
-	return (*refs.Address)(a).StableMarshal(nil)
-}
-
-var errCIDNotSet = errors.New("container ID is not set")
-var errOIDNotSet = errors.New("object ID is not set")
-
-// Unmarshal unmarshals protobuf binary representation of Address.
-func (a *Address) Unmarshal(data []byte) error {
-	err := (*refs.Address)(a).Unmarshal(data)
-	if err != nil {
-		return err
-	}
-
-	v2 := a.ToV2()
-
-	return checkFormat(v2)
-}
-
-// MarshalJSON encodes Address to protobuf JSON format.
-func (a *Address) MarshalJSON() ([]byte, error) {
-	return (*refs.Address)(a).MarshalJSON()
-}
-
-// UnmarshalJSON decodes Address from protobuf JSON format.
-func (a *Address) UnmarshalJSON(data []byte) error {
-	v2 := (*refs.Address)(a)
-
-	err := v2.UnmarshalJSON(data)
-	if err != nil {
-		return err
-	}
-
-	return checkFormat(v2)
-}
-
-func checkFormat(v2 *refs.Address) error {
-	var (
-		cID cid.ID
-		oID oid.ID
-	)
-
-	cidV2 := v2.GetContainerID()
-	if cidV2 == nil {
-		return errCIDNotSet
-	}
-
-	err := cID.ReadFromV2(*cidV2)
-	if err != nil {
-		return fmt.Errorf("could not convert V2 container ID: %w", err)
-	}
-
-	oidV2 := v2.GetObjectID()
-	if oidV2 == nil {
-		return errOIDNotSet
-	}
-
-	err = oID.ReadFromV2(*oidV2)
-	if err != nil {
-		return fmt.Errorf("could not convert V2 object ID: %w", err)
-	}
-
-	return nil
-}
diff --git a/object/address/address_test.go b/object/address/address_test.go
deleted file mode 100644
index 4d4a47f..0000000
--- a/object/address/address_test.go
+++ /dev/null
@@ -1,129 +0,0 @@
-package address
-
-import (
-	"strings"
-	"testing"
-
-	"github.com/nspcc-dev/neofs-api-go/v2/refs"
-	cidtest "github.com/nspcc-dev/neofs-sdk-go/container/id/test"
-	oidtest "github.com/nspcc-dev/neofs-sdk-go/object/id/test"
-	"github.com/stretchr/testify/require"
-)
-
-func TestAddress_SetContainerID(t *testing.T) {
-	a := NewAddress()
-
-	id := cidtest.ID()
-
-	a.SetContainerID(id)
-
-	cID, set := a.ContainerID()
-	require.True(t, set)
-	require.Equal(t, id, cID)
-}
-
-func TestAddress_SetObjectID(t *testing.T) {
-	a := NewAddress()
-
-	oid := oidtest.ID()
-
-	a.SetObjectID(oid)
-
-	oID, set := a.ObjectID()
-	require.True(t, set)
-	require.Equal(t, oid, oID)
-}
-
-func TestAddress_Parse(t *testing.T) {
-	cid := cidtest.ID()
-
-	oid := oidtest.ID()
-
-	t.Run("should parse successful", func(t *testing.T) {
-		s := strings.Join([]string{cid.String(), oid.String()}, addressSeparator)
-		a := NewAddress()
-
-		require.NoError(t, a.Parse(s))
-		oID, set := a.ObjectID()
-		require.True(t, set)
-		require.Equal(t, oid, oID)
-		cID, set := a.ContainerID()
-		require.True(t, set)
-		require.Equal(t, cid, cID)
-	})
-
-	t.Run("should fail for bad address", func(t *testing.T) {
-		s := strings.Join([]string{cid.String()}, addressSeparator)
-		require.EqualError(t, NewAddress().Parse(s), errInvalidAddressString.Error())
-	})
-
-	t.Run("should fail on container.ID", func(t *testing.T) {
-		s := strings.Join([]string{"1", "2"}, addressSeparator)
-		require.Error(t, NewAddress().Parse(s))
-	})
-
-	t.Run("should fail on object.ID", func(t *testing.T) {
-		s := strings.Join([]string{cid.String(), "2"}, addressSeparator)
-		require.Error(t, NewAddress().Parse(s))
-	})
-}
-
-func TestAddressEncoding(t *testing.T) {
-	a := NewAddress()
-	a.SetObjectID(oidtest.ID())
-	a.SetContainerID(cidtest.ID())
-
-	t.Run("binary", func(t *testing.T) {
-		data, err := a.Marshal()
-		require.NoError(t, err)
-
-		a2 := NewAddress()
-		require.NoError(t, a2.Unmarshal(data))
-
-		require.Equal(t, a, a2)
-	})
-
-	t.Run("json", func(t *testing.T) {
-		data, err := a.MarshalJSON()
-		require.NoError(t, err)
-
-		a2 := NewAddress()
-		require.NoError(t, a2.UnmarshalJSON(data))
-
-		require.Equal(t, a, a2)
-	})
-}
-
-func TestNewAddressFromV2(t *testing.T) {
-	t.Run("from nil", func(t *testing.T) {
-		var x *refs.Address
-
-		require.Nil(t, NewAddressFromV2(x))
-	})
-}
-
-func TestAddress_ToV2(t *testing.T) {
-	t.Run("nil", func(t *testing.T) {
-		var x *Address
-
-		require.Nil(t, x.ToV2())
-	})
-}
-
-func TestNewAddress(t *testing.T) {
-	t.Run("default values", func(t *testing.T) {
-		a := NewAddress()
-
-		// check initial values
-		_, set := a.ContainerID()
-		require.False(t, set)
-		_, set = a.ObjectID()
-		require.False(t, set)
-
-		// convert to v2 message
-		aV2 := a.ToV2()
-
-		require.Nil(t, aV2.GetContainerID())
-		require.Nil(t, aV2.GetObjectID())
-	})
-}
diff --git a/object/address/test/generate.go b/object/address/test/generate.go
deleted file mode 100644
index 224b5dd..0000000
--- a/object/address/test/generate.go
+++ /dev/null
@@ -1,17 +0,0 @@
-package address
-
-import (
-	cidtest "github.com/nspcc-dev/neofs-sdk-go/container/id/test"
-	"github.com/nspcc-dev/neofs-sdk-go/object/address"
-	oidtest "github.com/nspcc-dev/neofs-sdk-go/object/id/test"
-)
-
-// Address returns random object.Address.
-func Address() *address.Address {
-	x := address.NewAddress()
-
-	x.SetContainerID(cidtest.ID())
-	x.SetObjectID(oidtest.ID())
-
-	return x
-}
diff --git a/object/id/address.go b/object/id/address.go
new file mode 100644
index 0000000..4208a89
--- /dev/null
+++ b/object/id/address.go
@@ -0,0 +1,148 @@
+package oid
+
+import (
+	"errors"
+	"fmt"
+	"strings"
+
+	"github.com/nspcc-dev/neofs-api-go/v2/refs"
+	cid "github.com/nspcc-dev/neofs-sdk-go/container/id"
+)
+
+// Address represents global object identifier in NeoFS network. Each object
+// belongs to exactly one container and is uniquely addressed within the container.
+//
+// Address is mutually compatible with github.com/nspcc-dev/neofs-api-go/v2/refs.Address
+// message. See ReadFromV2 / WriteToV2 methods.
+//
+// Instances can be created using built-in var declaration.
+//
+// Note that direct typecast is not safe and may result in loss of compatibility:
+// 	_ = Address(refs.Address{}) // not recommended
+type Address struct {
+	cnr cid.ID
+
+	obj ID
+}
+
+// ReadFromV2 reads Address from the refs.Address message. Returns an error if
+// the message is malformed according to the NeoFS API V2 protocol.
+//
+// See also WriteToV2.
+func (x *Address) ReadFromV2(m refs.Address) error {
+	cnr := m.GetContainerID()
+	if cnr == nil {
+		return errors.New("missing container ID")
+	}
+
+	obj := m.GetObjectID()
+	if obj == nil {
+		return errors.New("missing object ID")
+	}
+
+	err := x.cnr.ReadFromV2(*cnr)
+	if err != nil {
+		return fmt.Errorf("invalid container ID: %w", err)
+	}
+
+	err = x.obj.ReadFromV2(*obj)
+	if err != nil {
+		return fmt.Errorf("invalid object ID: %w", err)
+	}
+
+	return nil
+}
+
+// WriteToV2 writes Address to the refs.Address message.
+// The message must not be nil.
+//
+// See also ReadFromV2.
+func (x Address) WriteToV2(m *refs.Address) {
+	var obj refs.ObjectID
+	x.obj.WriteToV2(&obj)
+
+	var cnr refs.ContainerID
+	x.cnr.WriteToV2(&cnr)
+
+	m.SetObjectID(&obj)
+	m.SetContainerID(&cnr)
+}
+
+// Container sets unique identifier of the NeoFS object container.
+//
+// Zero Address has zero container ID, which is incorrect according to NeoFS
+// API protocol.
+//
+// See also SetContainer.
+func (x Address) Container() cid.ID {
+	return x.cnr
+}
+
+// SetContainer sets unique identifier of the NeoFS object container.
+//
+// See also Container.
+func (x *Address) SetContainer(id cid.ID) {
+	x.cnr = id
+}
+
+// Object returns unique identifier of the object in the container
+// identified by Container().
+//
+// Zero Address has zero object ID, which is incorrect according to NeoFS
+// API protocol.
+//
+// See also SetObject.
+func (x Address) Object() ID {
+	return x.obj
+}
+
+// SetObject sets unique identifier of the object in the container
+// identified by Container().
+//
+// See also Object.
+func (x *Address) SetObject(id ID) {
+	x.obj = id
+}
+
+// delimiter of container and object IDs in Address protocol string.
+const idDelimiter = "/"
+
+// EncodeToString encodes Address into NeoFS API protocol string: concatenation
+// of the string-encoded container and object IDs delimited by a slash.
+//
+// See also DecodeString.
+func (x Address) EncodeToString() string {
+	return x.cnr.EncodeToString() + "/" + x.obj.EncodeToString()
+}
+
+// DecodeString decodes string into Address according to NeoFS API protocol. Returns
+// an error if s is malformed.
+//
+// See also DecodeString.
+func (x *Address) DecodeString(s string) error {
+	indDelimiter := strings.Index(s, idDelimiter)
+	if indDelimiter < 0 {
+		return errors.New("missing delimiter")
+	}
+
+	err := x.cnr.DecodeString(s[:indDelimiter])
+	if err != nil {
+		return fmt.Errorf("decode container string: %w", err)
+	}
+
+	err = x.obj.DecodeString(s[indDelimiter+1:])
+	if err != nil {
+		return fmt.Errorf("decode object string: %w", err)
+	}
+
+	return nil
+}
+
+// String implements fmt.Stringer.
+//
+// String is designed to be human-readable, and its format MAY differ between
+// SDK versions. String MAY return same result as EncodeToString. String MUST NOT
+// be used to encode Address into NeoFS protocol string.
+func (x Address) String() string {
+	return x.EncodeToString()
+}
diff --git a/object/id/address_test.go b/object/id/address_test.go
new file mode 100644
index 0000000..322707a
--- /dev/null
+++ b/object/id/address_test.go
@@ -0,0 +1,95 @@
+package oid_test
+
+import (
+	"testing"
+
+	"github.com/nspcc-dev/neofs-api-go/v2/refs"
+	cidtest "github.com/nspcc-dev/neofs-sdk-go/container/id/test"
+	oid "github.com/nspcc-dev/neofs-sdk-go/object/id"
+	oidtest "github.com/nspcc-dev/neofs-sdk-go/object/id/test"
+	"github.com/stretchr/testify/require"
+)
+
+func TestAddress_SetContainer(t *testing.T) {
+	var x oid.Address
+
+	require.Zero(t, x.Container())
+
+	cnr := cidtest.ID()
+
+	x.SetContainer(cnr)
+	require.Equal(t, cnr, x.Container())
+}
+
+func TestAddress_SetObject(t *testing.T) {
+	var x oid.Address
+
+	require.Zero(t, x.Object())
+
+	obj := oidtest.ID()
+
+	x.SetObject(obj)
+	require.Equal(t, obj, x.Object())
+}
+
+func TestAddress_ReadFromV2(t *testing.T) {
+	var x oid.Address
+	var xV2 refs.Address
+
+	require.Error(t, x.ReadFromV2(xV2))
+
+	var cnrV2 refs.ContainerID
+	xV2.SetContainerID(&cnrV2)
+
+	require.Error(t, x.ReadFromV2(xV2))
+
+	cnr := cidtest.ID()
+	cnr.WriteToV2(&cnrV2)
+
+	require.Error(t, x.ReadFromV2(xV2))
+
+	var objV2 refs.ObjectID
+	xV2.SetObjectID(&objV2)
+
+	require.Error(t, x.ReadFromV2(xV2))
+
+	obj := oidtest.ID()
+	obj.WriteToV2(&objV2)
+
+	require.NoError(t, x.ReadFromV2(xV2))
+	require.Equal(t, cnr, x.Container())
+	require.Equal(t, obj, x.Object())
+
+	var xV2To refs.Address
+	x.WriteToV2(&xV2To)
+
+	require.Equal(t, xV2, xV2To)
+}
+
+func TestAddress_DecodeString(t *testing.T) {
+	var x, x2 oid.Address
+
+	require.NoError(t, x2.DecodeString(x.EncodeToString()))
+	require.Equal(t, x, x2)
+
+	cnr := cidtest.ID()
+	obj := oidtest.ID()
+
+	x.SetContainer(cnr)
+	x.SetObject(obj)
+
+	require.NoError(t, x2.DecodeString(x.EncodeToString()))
+	require.Equal(t, x, x2)
+
+	strCnr := cnr.EncodeToString()
+	strObj := obj.EncodeToString()
+
+	require.Error(t, x2.DecodeString(""))
+	require.Error(t, x2.DecodeString("/"))
+	require.Error(t, x2.DecodeString(strCnr))
+	require.Error(t, x2.DecodeString(strCnr+"/"))
+	require.Error(t, x2.DecodeString("/"+strCnr))
+	require.Error(t, x2.DecodeString(strCnr+strObj))
+	require.Error(t, x2.DecodeString(strCnr+"\\"+strObj))
+	require.NoError(t, x2.DecodeString(strCnr+"/"+strObj))
+}
diff --git a/object/id/doc.go b/object/id/doc.go
index 89f1585..0117742 100644
--- a/object/id/doc.go
+++ b/object/id/doc.go
@@ -1,6 +1,9 @@
 /*
 Package oid provides primitives to work with object identification in NeoFS.
 
+Address type is used for global object identity inside the NeoFS network,
+while ID represents identity within a fixed container.
+
 Using package types in an application is recommended to potentially work with
 different protocol versions with which these types are compatible.
 
diff --git a/object/id/id.go b/object/id/id.go
index 7fbd8b6..f9ccbe9 100644
--- a/object/id/id.go
+++ b/object/id/id.go
@@ -19,7 +19,7 @@ import (
 // Instances can be created using built-in var declaration.
 //
 // Note that direct typecast is not safe and may result in loss of compatibility:
-// 	_ = ObjectID([32]byte{}) // not recommended
+// 	_ = ID([32]byte{}) // not recommended
 type ID [sha256.Size]byte
 
 // ReadFromV2 reads ID from the refs.ObjectID message. Returns an error if
diff --git a/object/id/test/doc.go b/object/id/test/doc.go
index 22d5e2e..4aad5e7 100644
--- a/object/id/test/doc.go
+++ b/object/id/test/doc.go
@@ -6,7 +6,7 @@ Note that importing the package into source files is highly discouraged.
 Random instance generation functions can be useful when testing expects any value, e.g.:
 	import oidtest "github.com/nspcc-dev/neofs-sdk-go/object/id/test"
 
-	dec := oidtest.ID()
+	value := oidtest.ID()
 	// test the value
 
 */
diff --git a/object/id/test/generate.go b/object/id/test/generate.go
index 8bb8032..8a7e035 100644
--- a/object/id/test/generate.go
+++ b/object/id/test/generate.go
@@ -4,10 +4,11 @@ import (
 	"crypto/sha256"
 	"math/rand"
 
+	cidtest "github.com/nspcc-dev/neofs-sdk-go/container/id/test"
 	oid "github.com/nspcc-dev/neofs-sdk-go/object/id"
 )
 
-// ID returns random object.ID.
+// ID returns random oid.ID.
 func ID() oid.ID {
 	checksum := [sha256.Size]byte{}
 
@@ -16,7 +17,7 @@ func ID() oid.ID {
 	return idWithChecksum(checksum)
 }
 
-// idWithChecksum returns object.ID initialized
+// idWithChecksum returns oid.ID initialized
 // with specified checksum.
 func idWithChecksum(cs [sha256.Size]byte) oid.ID {
 	var id oid.ID
@@ -24,3 +25,13 @@ func idWithChecksum(cs [sha256.Size]byte) oid.ID {
 
 	return id
 }
+
+// Address returns random object.Address.
+func Address() oid.Address {
+	var x oid.Address
+
+	x.SetContainer(cidtest.ID())
+	x.SetObject(ID())
+
+	return x
+}
diff --git a/pool/pool.go b/pool/pool.go
index bcfda9a..10c628d 100644
--- a/pool/pool.go
+++ b/pool/pool.go
@@ -25,7 +25,6 @@ import (
 	"github.com/nspcc-dev/neofs-sdk-go/eacl"
 	"github.com/nspcc-dev/neofs-sdk-go/netmap"
 	"github.com/nspcc-dev/neofs-sdk-go/object"
-	"github.com/nspcc-dev/neofs-sdk-go/object/address"
 	oid "github.com/nspcc-dev/neofs-sdk-go/object/id"
 	"github.com/nspcc-dev/neofs-sdk-go/session"
 	"github.com/nspcc-dev/neofs-sdk-go/user"
@@ -293,14 +292,8 @@ func (c *clientWrapper) objectPut(ctx context.Context, prm PrmObjectPut) (*oid.I
 
 func (c *clientWrapper) objectDelete(ctx context.Context, prm PrmObjectDelete) error {
 	var cliPrm sdkClient.PrmObjectDelete
-
-	if cnr, set := prm.addr.ContainerID(); set {
-		cliPrm.FromContainer(cnr)
-	}
-
-	if obj, set := prm.addr.ObjectID(); set {
-		cliPrm.ByID(obj)
-	}
+	cliPrm.FromContainer(prm.addr.Container())
+	cliPrm.ByID(prm.addr.Object())
 
 	if prm.stoken != nil {
 		cliPrm.WithinSession(*prm.stoken)
@@ -319,22 +312,8 @@ func (c *clientWrapper) objectDelete(ctx context.Context, prm PrmObjectDelete) e
 
 func (c *clientWrapper) objectGet(ctx context.Context, prm PrmObjectGet) (*ResGetObject, error) {
 	var cliPrm sdkClient.PrmObjectGet
-
-	if cnr, set := prm.addr.ContainerID(); set {
-		cliPrm.FromContainer(cnr)
-	}
-
-	if obj, set := prm.addr.ObjectID(); set {
-		cliPrm.ByID(obj)
-	}
-
-	if cnr, set := prm.addr.ContainerID(); set {
-		cliPrm.FromContainer(cnr)
-	}
-
-	if obj, set := prm.addr.ObjectID(); set {
-		cliPrm.ByID(obj)
-	}
+	cliPrm.FromContainer(prm.addr.Container())
+	cliPrm.ByID(prm.addr.Object())
 
 	if prm.stoken != nil {
 		cliPrm.WithinSession(*prm.stoken)
@@ -367,14 +346,8 @@ func (c *clientWrapper) objectGet(ctx context.Context, prm PrmObjectGet) (*ResGe
 
 func (c *clientWrapper) objectHead(ctx context.Context, prm PrmObjectHead) (*object.Object, error) {
 	var cliPrm sdkClient.PrmObjectHead
-
-	if cnr, set := prm.addr.ContainerID(); set {
-		cliPrm.FromContainer(cnr)
-	}
-
-	if obj, set := prm.addr.ObjectID(); set {
-		cliPrm.ByID(obj)
-	}
+	cliPrm.FromContainer(prm.addr.Container())
+	cliPrm.ByID(prm.addr.Object())
 
 	if prm.stoken != nil {
 		cliPrm.WithinSession(*prm.stoken)
@@ -403,18 +376,11 @@ func (c *clientWrapper) objectHead(ctx context.Context, prm PrmObjectHead) (*obj
 
 func (c *clientWrapper) objectRange(ctx context.Context, prm PrmObjectRange) (*ResObjectRange, error) {
 	var cliPrm sdkClient.PrmObjectRange
-
+	cliPrm.FromContainer(prm.addr.Container())
+	cliPrm.ByID(prm.addr.Object())
 	cliPrm.SetOffset(prm.off)
 	cliPrm.SetLength(prm.ln)
 
-	if cnr, set := prm.addr.ContainerID(); set {
-		cliPrm.FromContainer(cnr)
-	}
-
-	if obj, set := prm.addr.ObjectID(); set {
-		cliPrm.ByID(obj)
-	}
-
 	if prm.stoken != nil {
 		cliPrm.WithinSession(*prm.stoken)
 	}
@@ -609,15 +575,24 @@ type clientPack struct {
 type prmContext struct {
 	defaultSession bool
 	verb           session.ObjectVerb
-	addr           address.Address
+	cnr            cid.ID
+
+	objSet bool
+	obj    oid.ID
 }
 
 func (x *prmContext) useDefaultSession() {
 	x.defaultSession = true
 }
 
-func (x *prmContext) useAddress(addr address.Address) {
-	x.addr = addr
+func (x *prmContext) useContainer(cnr cid.ID) {
+	x.cnr = cnr
+}
+
+func (x *prmContext) useAddress(addr oid.Address) {
+	x.cnr = addr.Container()
+	x.obj = addr.Object()
+	x.objSet = true
 }
 
 func (x *prmContext) useVerb(verb session.ObjectVerb) {
@@ -669,11 +644,11 @@ func (x *PrmObjectPut) SetPayload(payload io.Reader) {
 type PrmObjectDelete struct {
 	prmCommon
 
-	addr address.Address
+	addr oid.Address
 }
 
 // SetAddress specifies NeoFS address of the object.
-func (x *PrmObjectDelete) SetAddress(addr address.Address) {
+func (x *PrmObjectDelete) SetAddress(addr oid.Address) {
 	x.addr = addr
 }
 
@@ -681,11 +656,11 @@ func (x *PrmObjectDelete) SetAddress(addr address.Address) {
 type PrmObjectGet struct {
 	prmCommon
 
-	addr address.Address
+	addr oid.Address
 }
 
 // SetAddress specifies NeoFS address of the object.
-func (x *PrmObjectGet) SetAddress(addr address.Address) {
+func (x *PrmObjectGet) SetAddress(addr oid.Address) {
 	x.addr = addr
 }
 
@@ -693,11 +668,11 @@ func (x *PrmObjectGet) SetAddress(addr address.Address) {
 type PrmObjectHead struct {
 	prmCommon
 
-	addr address.Address
+	addr oid.Address
 }
 
 // SetAddress specifies NeoFS address of the object.
-func (x *PrmObjectHead) SetAddress(addr address.Address) {
+func (x *PrmObjectHead) SetAddress(addr oid.Address) {
 	x.addr = addr
 }
 
@@ -705,12 +680,12 @@ func (x *PrmObjectHead) SetAddress(addr address.Address) {
 type PrmObjectRange struct {
 	prmCommon
 
-	addr    address.Address
+	addr    oid.Address
 	off, ln uint64
 }
 
 // SetAddress specifies NeoFS address of the object.
-func (x *PrmObjectRange) SetAddress(addr address.Address) {
+func (x *PrmObjectRange) SetAddress(addr oid.Address) {
 	x.addr = addr
 }
 
@@ -1283,7 +1258,9 @@ type callContext struct {
 	sessionDefault bool
 	sessionTarget  func(session.Object)
 	sessionVerb    session.ObjectVerb
-	sessionAddr    address.Address
+	sessionCnr     cid.ID
+	sessionObjSet  bool
+	sessionObj     oid.ID
 }
 
 func (p *Pool) initCallContext(ctx *callContext, cfg prmCommon, prmCtx prmContext) error {
@@ -1309,7 +1286,9 @@ func (p *Pool) initCallContext(ctx *callContext, cfg prmCommon, prmCtx prmContex
 	ctx.sessionDefault = cfg.stoken == nil && prmCtx.defaultSession
 	if ctx.sessionDefault {
 		ctx.sessionVerb = prmCtx.verb
-		ctx.sessionAddr = prmCtx.addr
+		ctx.sessionCnr = prmCtx.cnr
+		ctx.sessionObjSet = prmCtx.objSet
+		ctx.sessionObj = prmCtx.obj
 	}
 
 	return err
@@ -1333,7 +1312,11 @@ func (p *Pool) openDefaultSession(ctx *callContext) error {
 	}
 
 	tok.ForVerb(ctx.sessionVerb)
-	tok.ApplyTo(ctx.sessionAddr)
+	tok.BindContainer(ctx.sessionCnr)
+
+	if ctx.sessionObjSet {
+		tok.LimitByObject(ctx.sessionObj)
+	}
 
 	// sign the token
 	if err := tok.Sign(*ctx.key); err != nil {
@@ -1372,15 +1355,12 @@ func (p *Pool) fillAppropriateKey(prm *prmCommon) {
 
 // PutObject writes an object through a remote server using NeoFS API protocol.
 func (p *Pool) PutObject(ctx context.Context, prm PrmObjectPut) (*oid.ID, error) {
-	var cIDp *cid.ID
-	if cID, set := prm.hdr.ContainerID(); set {
-		cIDp = &cID
-	}
+	cnr, _ := prm.hdr.ContainerID()
 
 	var prmCtx prmContext
 	prmCtx.useDefaultSession()
 	prmCtx.useVerb(session.VerbObjectPut)
-	prmCtx.useAddress(*newAddressFromCnrID(cIDp))
+	prmCtx.useContainer(cnr)
 
 	p.fillAppropriateKey(&prm.prmCommon)
 
@@ -1604,7 +1584,7 @@ func (p *Pool) SearchObjects(ctx context.Context, prm PrmObjectSearch) (*ResObje
 	var prmCtx prmContext
 	prmCtx.useDefaultSession()
 	prmCtx.useVerb(session.VerbObjectSearch)
-	prmCtx.useAddress(*newAddressFromCnrID(&prm.cnrID))
+	prmCtx.useContainer(prm.cnrID)
 
 	p.fillAppropriateKey(&prm.prmCommon)
 
@@ -1795,11 +1775,3 @@ func (p *Pool) Close() {
 	p.cancel()
 	<-p.closedCh
 }
-
-func newAddressFromCnrID(cnrID *cid.ID) *address.Address {
-	addr := address.NewAddress()
-	if cnrID != nil {
-		addr.SetContainerID(*cnrID)
-	}
-	return addr
-}
diff --git a/pool/pool_test.go b/pool/pool_test.go
index d76d816..49dcbb5 100644
--- a/pool/pool_test.go
+++ b/pool/pool_test.go
@@ -17,7 +17,7 @@ import (
 	neofsecdsa "github.com/nspcc-dev/neofs-sdk-go/crypto/ecdsa"
 	"github.com/nspcc-dev/neofs-sdk-go/netmap"
 	"github.com/nspcc-dev/neofs-sdk-go/object"
-	"github.com/nspcc-dev/neofs-sdk-go/object/address"
+	oid "github.com/nspcc-dev/neofs-sdk-go/object/id"
 	"github.com/nspcc-dev/neofs-sdk-go/session"
 	"github.com/nspcc-dev/neofs-sdk-go/user"
 	"github.com/stretchr/testify/require"
@@ -418,7 +418,7 @@ func TestSessionCache(t *testing.T) {
 	require.True(t, containsTokens(tokens, &st))
 
 	var prm PrmObjectGet
-	prm.SetAddress(address.Address{})
+	prm.SetAddress(oid.Address{})
 	prm.UseSession(session.Object{})
 
 	_, err = pool.GetObject(ctx, prm)
@@ -565,7 +565,7 @@ func TestSessionCacheWithKey(t *testing.T) {
 	require.True(t, containsTokens(tokens, &st))
 
 	var prm PrmObjectGet
-	prm.SetAddress(address.Address{})
+	prm.SetAddress(oid.Address{})
 	prm.UseKey(newPrivateKey(t))
 
 	_, err = pool.GetObject(ctx, prm)
diff --git a/session/container.go b/session/container.go
index 747afc3..88f3062 100644
--- a/session/container.go
+++ b/session/container.go
@@ -57,7 +57,7 @@ func (x *Container) ReadFromV2(m session.Token) error {
 	}
 
 	c, ok := b.GetContext().(*session.ContainerSessionContext)
-	if !ok {
+	if !ok || c == nil {
 		return fmt.Errorf("invalid context %T", b.GetContext())
 	}
 
@@ -70,11 +70,7 @@ func (x *Container) ReadFromV2(m session.Token) error {
 
 	x.body = *b
 
-	if c != nil {
-		x.c = *c
-	} else {
-		x.c = session.ContainerSessionContext{}
-	}
+	x.c = *c
 
 	lt := b.GetLifetime()
 	if lt != nil {
diff --git a/session/object.go b/session/object.go
index d8a7fa1..5c5a8a6 100644
--- a/session/object.go
+++ b/session/object.go
@@ -9,9 +9,10 @@ import (
 	"github.com/google/uuid"
 	"github.com/nspcc-dev/neofs-api-go/v2/refs"
 	"github.com/nspcc-dev/neofs-api-go/v2/session"
+	cid "github.com/nspcc-dev/neofs-sdk-go/container/id"
 	neofscrypto "github.com/nspcc-dev/neofs-sdk-go/crypto"
 	neofsecdsa "github.com/nspcc-dev/neofs-sdk-go/crypto/ecdsa"
-	"github.com/nspcc-dev/neofs-sdk-go/object/address"
+	oid "github.com/nspcc-dev/neofs-sdk-go/object/id"
 	"github.com/nspcc-dev/neofs-sdk-go/user"
 )
 
@@ -57,26 +58,23 @@ func (x *Object) ReadFromV2(m session.Token) error {
 	}
 
 	c, ok := b.GetContext().(*session.ObjectSessionContext)
-	if !ok {
+	if !ok || c == nil {
 		return fmt.Errorf("invalid context %T", b.GetContext())
 	}
 
 	x.body = *b
 
-	if c != nil {
-		x.c = *c
+	x.c = *c
 
-		obj := c.GetAddress()
-		if obj != nil {
-			x.obj = *obj
-		} else {
-			x.obj = refs.Address{}
-		}
-	} else {
-		x.c = session.ObjectSessionContext{}
-		x.obj = refs.Address{}
+	obj := c.GetAddress()
+
+	cnr := obj.GetContainerID()
+	if cnr == nil {
+		return errors.New("missing bound container")
 	}
 
+	x.obj = *obj
+
 	lt := b.GetLifetime()
 	if lt != nil {
 		x.lt = *lt
@@ -209,23 +207,63 @@ func (x Object) VerifySignature() bool {
 	return x.sig.Verify(data)
 }
 
-// ApplyTo limits session scope to a given author object.
+// BindContainer binds the Object session to a given container. Each session
+// MUST be bound to exactly one container.
 //
-// See also AppliedTo.
-func (x *Object) ApplyTo(a address.Address) {
-	x.obj = *a.ToV2()
+// See also AssertContainer.
+func (x *Object) BindContainer(cnr cid.ID) {
+	var cnrV2 refs.ContainerID
+	cnr.WriteToV2(&cnrV2)
+
+	x.obj.SetContainerID(&cnrV2)
 }
 
-// AppliedTo checks if session scope is limited by a given object.
+// AssertContainer checks if Object session bound to a given container.
 //
-// Zero Object isn't applied to any author's object.
+// Zero Object isn't bound to any container which is incorrect according to
+// NeoFS API protocol.
 //
-// See also ApplyTo.
-func (x Object) AppliedTo(obj address.Address) bool {
-	objv2 := *address.NewAddressFromV2(&x.obj)
+// See also BindContainer.
+func (x Object) AssertContainer(cnr cid.ID) bool {
+	cnrV2 := x.obj.GetContainerID()
+	if cnrV2 == nil {
+		return false
+	}
 
-	// FIXME: use Equals method
-	return obj.String() == objv2.String()
+	var cnr2 cid.ID
+
+	err := cnr2.ReadFromV2(*cnrV2)
+
+	return err == nil && cnr2.Equals(cnr)
+}
+
+// LimitByObject limits session scope to a given object from the container
+// to which Object session is bound.
+//
+// See also AssertObject.
+func (x *Object) LimitByObject(obj oid.ID) {
+	var objV2 refs.ObjectID
+	obj.WriteToV2(&objV2)
+
+	x.obj.SetObjectID(&objV2)
+}
+
+// AssertObject checks if Object session is applied to a given object.
+//
+// Zero Object is applied to all objects in the container.
+//
+// See also LimitByObject.
+func (x Object) AssertObject(obj oid.ID) bool {
+	objV2 := x.obj.GetObjectID()
+	if objV2 == nil {
+		return true
+	}
+
+	var obj2 oid.ID
+
+	err := obj2.ReadFromV2(*objV2)
+
+	return err == nil && obj2.Equals(obj)
 }
 
 // ObjectVerb enumerates object operations.
diff --git a/session/object_test.go b/session/object_test.go
index c702c1c..00cc0a8 100644
--- a/session/object_test.go
+++ b/session/object_test.go
@@ -9,11 +9,12 @@ import (
 
 	"github.com/google/uuid"
 	"github.com/nspcc-dev/neo-go/pkg/crypto/keys"
+	"github.com/nspcc-dev/neofs-api-go/v2/refs"
 	v2session "github.com/nspcc-dev/neofs-api-go/v2/session"
+	cidtest "github.com/nspcc-dev/neofs-sdk-go/container/id/test"
 	neofscrypto "github.com/nspcc-dev/neofs-sdk-go/crypto"
 	neofsecdsa "github.com/nspcc-dev/neofs-sdk-go/crypto/ecdsa"
-	"github.com/nspcc-dev/neofs-sdk-go/object/address"
-	addresstest "github.com/nspcc-dev/neofs-sdk-go/object/address/test"
+	oidtest "github.com/nspcc-dev/neofs-sdk-go/object/id/test"
 	"github.com/nspcc-dev/neofs-sdk-go/session"
 	sessiontest "github.com/nspcc-dev/neofs-sdk-go/session/test"
 	"github.com/nspcc-dev/neofs-sdk-go/user"
@@ -41,6 +42,14 @@ func TestObject_ReadFromV2(t *testing.T) {
 	var c v2session.ObjectSessionContext
 	id := uuid.New()
 
+	cnr := cidtest.ID()
+
+	var cnrV2 refs.ContainerID
+	cnr.WriteToV2(&cnrV2)
+
+	var addrV2 refs.Address
+	addrV2.SetContainerID(&cnrV2)
+
 	t.Run("protocol violation", func(t *testing.T) {
 		require.Error(t, x.ReadFromV2(m))
 
@@ -54,27 +63,32 @@ func TestObject_ReadFromV2(t *testing.T) {
 
 		b.SetContext(&c)
 
+		require.Error(t, x.ReadFromV2(m))
+
+		c.SetAddress(&addrV2)
+
 		require.NoError(t, x.ReadFromV2(m))
 	})
 
 	m.SetBody(&b)
+	c.SetAddress(&addrV2)
 	b.SetContext(&c)
 	b.SetID(id[:])
 
 	t.Run("object", func(t *testing.T) {
-		var obj address.Address
+		require.NoError(t, x.ReadFromV2(m))
+		require.True(t, x.AssertContainer(cnr))
+
+		obj := oidtest.Address()
+
+		var objV2 refs.Address
+		obj.WriteToV2(&objV2)
+
+		c.SetAddress(&objV2)
 
 		require.NoError(t, x.ReadFromV2(m))
-		require.True(t, x.AppliedTo(obj))
-
-		obj = *addresstest.Address()
-
-		objv2 := *obj.ToV2()
-
-		c.SetAddress(&objv2)
-
-		require.NoError(t, x.ReadFromV2(m))
-		require.True(t, x.AppliedTo(obj))
+		require.True(t, x.AssertContainer(obj.Container()))
+		require.True(t, x.AssertObject(obj.Object()))
 	})
 
 	t.Run("verb", func(t *testing.T) {
@@ -157,16 +171,31 @@ func TestEncodingObject(t *testing.T) {
 	})
 }
 
-func TestObjectAppliedTo(t *testing.T) {
+func TestObject_BindContainer(t *testing.T) {
 	var x session.Object
 
-	a := *addresstest.Address()
+	cnr := cidtest.ID()
 
-	require.False(t, x.AppliedTo(a))
+	require.False(t, x.AssertContainer(cnr))
 
-	x.ApplyTo(a)
+	x.BindContainer(cnr)
 
-	require.True(t, x.AppliedTo(a))
+	require.True(t, x.AssertContainer(cnr))
+}
+
+func TestObject_LimitByObject(t *testing.T) {
+	var x session.Object
+
+	obj := oidtest.ID()
+	obj2 := oidtest.ID()
+
+	require.True(t, x.AssertObject(obj))
+	require.True(t, x.AssertObject(obj2))
+
+	x.LimitByObject(obj)
+
+	require.True(t, x.AssertObject(obj))
+	require.False(t, x.AssertObject(obj2))
 }
 
 func TestObjectExp(t *testing.T) {
@@ -250,7 +279,8 @@ func TestObjectSignature(t *testing.T) {
 	const exp = 33
 	id := uuid.New()
 	key := randPublicKey()
-	obj := *addresstest.Address()
+	cnr := cidtest.ID()
+	obj := oidtest.ID()
 	verb := session.VerbObjectDelete
 
 	signer := randSigner()
@@ -275,8 +305,11 @@ func TestObjectSignature(t *testing.T) {
 		func() { x.SetAuthKey(key) },
 		func() { x.SetAuthKey(randPublicKey()) },
 
-		func() { x.ApplyTo(obj) },
-		func() { x.ApplyTo(*addresstest.Address()) },
+		func() { x.BindContainer(cnr) },
+		func() { x.BindContainer(cidtest.ID()) },
+
+		func() { x.LimitByObject(obj) },
+		func() { x.LimitByObject(oidtest.ID()) },
 
 		func() { x.ForVerb(verb) },
 		func() { x.ForVerb(verb + 1) },
diff --git a/session/test/session.go b/session/test/session.go
index fb2031f..fb5a8d8 100644
--- a/session/test/session.go
+++ b/session/test/session.go
@@ -9,7 +9,7 @@ import (
 	"github.com/nspcc-dev/neo-go/pkg/crypto/keys"
 	cidtest "github.com/nspcc-dev/neofs-sdk-go/container/id/test"
 	neofsecdsa "github.com/nspcc-dev/neofs-sdk-go/crypto/ecdsa"
-	addresstest "github.com/nspcc-dev/neofs-sdk-go/object/address/test"
+	oidtest "github.com/nspcc-dev/neofs-sdk-go/object/id/test"
 	"github.com/nspcc-dev/neofs-sdk-go/session"
 )
 
@@ -71,8 +71,11 @@ func Object() *session.Object {
 		panic(err)
 	}
 
+	addr := oidtest.Address()
+
 	tok.ForVerb(session.VerbObjectPut)
-	tok.ApplyTo(*addresstest.Address())
+	tok.BindContainer(addr.Container())
+	tok.LimitByObject(addr.Object())
 	tok.SetID(uuid.New())
 	tok.SetAuthKey((*neofsecdsa.PublicKey)(&priv.PublicKey))
 	tok.SetExp(11)