diff --git a/pkg/services/object_manager/placement/traverser.go b/pkg/services/object_manager/placement/traverser.go
index d9ce2eef3..b578bf0a4 100644
--- a/pkg/services/object_manager/placement/traverser.go
+++ b/pkg/services/object_manager/placement/traverser.go
@@ -35,7 +35,9 @@ type Traverser struct {
 }
 
 type cfg struct {
-	rem int
+	trackCopies bool
+
+	flatSuccess *uint32
 
 	addr *object.Address
 
@@ -52,7 +54,8 @@ var errNilPolicy = errors.New("placement policy is nil")
 
 func defaultCfg() *cfg {
 	return &cfg{
-		addr: object.NewAddress(),
+		trackCopies: true,
+		addr:        object.NewAddress(),
 	}
 }
 
@@ -77,17 +80,21 @@ func NewTraverser(opts ...Option) (*Traverser, error) {
 		return nil, errors.Wrap(err, "could not build placement")
 	}
 
-	rs := cfg.policy.Replicas()
-	rem := make([]int, 0, len(rs))
+	var rem []int
+	if cfg.flatSuccess != nil {
+		ns = flatNodes(ns)
+		rem = []int{int(*cfg.flatSuccess)}
+	} else {
+		rs := cfg.policy.Replicas()
+		rem = make([]int, 0, len(rs))
 
-	for i := range rs {
-		cnt := cfg.rem
-
-		if cnt == 0 {
-			cnt = int(rs[i].Count())
+		for i := range rs {
+			if cfg.trackCopies {
+				rem = append(rem, int(rs[i].Count()))
+			} else {
+				rem = append(rem, -1)
+			}
 		}
-
-		rem = append(rem, cnt)
 	}
 
 	return &Traverser{
@@ -97,6 +104,20 @@ func NewTraverser(opts ...Option) (*Traverser, error) {
 	}, nil
 }
 
+func flatNodes(ns []netmap.Nodes) []netmap.Nodes {
+	sz := 0
+	for i := range ns {
+		sz += len(ns[i])
+	}
+
+	flat := make(netmap.Nodes, 0, sz)
+	for i := range ns {
+		flat = append(flat, ns[i]...)
+	}
+
+	return []netmap.Nodes{flat}
+}
+
 // Next returns next unprocessed address of the object placement.
 //
 // Returns nil if no nodes left or traversal operation succeeded.
@@ -193,13 +214,13 @@ func ForObject(id *object.ID) Option {
 	}
 }
 
-// SuccessAfter is a success number setting option.
+// SuccessAfter is a flat success number setting option.
 //
 // Option has no effect if the number is not positive.
-func SuccessAfter(v int) Option {
+func SuccessAfter(v uint32) Option {
 	return func(c *cfg) {
 		if v > 0 {
-			c.rem = v
+			c.flatSuccess = &v
 		}
 	}
 }
@@ -207,6 +228,6 @@ func SuccessAfter(v int) Option {
 // WithoutSuccessTracking disables success tracking in traversal.
 func WithoutSuccessTracking() Option {
 	return func(c *cfg) {
-		c.rem = -1
+		c.trackCopies = false
 	}
 }
diff --git a/pkg/services/object_manager/placement/traverser_test.go b/pkg/services/object_manager/placement/traverser_test.go
index 5f8e91ead..42a427f68 100644
--- a/pkg/services/object_manager/placement/traverser_test.go
+++ b/pkg/services/object_manager/placement/traverser_test.go
@@ -7,6 +7,7 @@ import (
 	"github.com/nspcc-dev/neofs-api-go/pkg/container"
 	"github.com/nspcc-dev/neofs-api-go/pkg/netmap"
 	"github.com/nspcc-dev/neofs-api-go/pkg/object"
+	"github.com/nspcc-dev/neofs-node/pkg/network"
 	"github.com/stretchr/testify/require"
 )
 
@@ -114,34 +115,21 @@ func TestTraverserObjectScenarios(t *testing.T) {
 
 		tr, err := NewTraverser(
 			ForContainer(cnr),
-			UseBuilder(&testBuilder{vectors: nodesCopy}),
+			UseBuilder(&testBuilder{
+				vectors: nodesCopy,
+			}),
 			SuccessAfter(1),
 		)
 		require.NoError(t, err)
 
-		fn := func(curVector int) {
-			for i := 0; i < selectors[curVector]; i++ {
-				addrs := tr.Next()
-				require.Len(t, addrs, 1)
-
-				require.Equal(t, nodes[curVector][i].Address(), addrs[0].String())
-			}
-
-			require.Empty(t, tr.Next())
-			require.False(t, tr.Success())
-
-			tr.SubmitSuccess()
+		for i := 0; i < len(nodes[0]); i++ {
+			require.NotNil(t, tr.Next())
 		}
 
-		for i := range selectors {
-			fn(i)
+		n, err := network.AddressFromString(nodes[1][0].Address())
+		require.NoError(t, err)
 
-			if i < len(selectors)-1 {
-				require.False(t, tr.Success())
-			} else {
-				require.True(t, tr.Success())
-			}
-		}
+		require.Equal(t, []*network.Address{n}, tr.Next())
 	})
 
 	t.Run("put scenario", func(t *testing.T) {
@@ -186,4 +174,32 @@ func TestTraverserObjectScenarios(t *testing.T) {
 			}
 		}
 	})
+
+	t.Run("local operation scenario", func(t *testing.T) {
+		selectors := []int{2, 3}
+		replicas := []int{1, 2}
+
+		nodes, cnr := testPlacement(t, selectors, replicas)
+
+		tr, err := NewTraverser(
+			ForContainer(cnr),
+			UseBuilder(&testBuilder{
+				vectors: []netmap.Nodes{{nodes[1][1]}}, // single node (local)
+			}),
+			SuccessAfter(1),
+		)
+		require.NoError(t, err)
+
+		require.NotEmpty(t, tr.Next())
+		require.False(t, tr.Success())
+
+		// add 1 OK
+		tr.SubmitSuccess()
+
+		// nothing more to do
+		require.Empty(t, tr.Next())
+
+		// common success
+		require.True(t, tr.Success())
+	})
 }