diff --git a/internal/handler/handler_test.go b/internal/handler/handler_test.go
index 81d9784..dbb037d 100644
--- a/internal/handler/handler_test.go
+++ b/internal/handler/handler_test.go
@@ -26,6 +26,7 @@ import (
 	"git.frostfs.info/TrueCloudLab/frostfs-sdk-go/netmap"
 	"git.frostfs.info/TrueCloudLab/frostfs-sdk-go/object"
 	oid "git.frostfs.info/TrueCloudLab/frostfs-sdk-go/object/id"
+	oidtest "git.frostfs.info/TrueCloudLab/frostfs-sdk-go/object/id/test"
 	"git.frostfs.info/TrueCloudLab/frostfs-sdk-go/user"
 	"github.com/nspcc-dev/neo-go/pkg/crypto/keys"
 	"github.com/panjf2000/ants/v2"
@@ -64,6 +65,7 @@ func (t *treeServiceMock) GetLatestVersion(context.Context, *cid.ID, string) (*d
 type configMock struct {
 	additionalFilenameSearch bool
 	additionalSlashSearch    bool
+	indexEnabled             bool
 	cors                     *data.CORSRule
 }
 
@@ -76,7 +78,7 @@ func (c *configMock) ArchiveCompression() bool {
 }
 
 func (c *configMock) IndexPageEnabled() bool {
-	return false
+	return c.indexEnabled
 }
 
 func (c *configMock) IndexPageTemplate() string {
@@ -259,6 +261,7 @@ func TestBasic(t *testing.T) {
 	err = json.Unmarshal(r.Response.Body(), &putRes)
 	require.NoError(t, err)
 
+	hc.cfg.additionalFilenameSearch = true
 	obj := hc.frostfs.objects[putRes.ContainerID+"/"+putRes.ObjectID]
 	fileName := prepareObjectAttributes(object.AttributeFileName, objFileName)
 	filePath := prepareObjectAttributes(object.AttributeFilePath, objFilePath)
@@ -269,6 +272,14 @@ func TestBasic(t *testing.T) {
 		r = prepareGetRequest(ctx, cnrID.EncodeToString(), putRes.ObjectID)
 		hc.Handler().DownloadByAddressOrBucketName(r)
 		require.Equal(t, content, string(r.Response.Body()))
+
+		r = prepareGetRequest(ctx, cnrID.EncodeToString(), objFilePath)
+		hc.Handler().DownloadByAddressOrBucketName(r)
+		require.Equal(t, content, string(r.Response.Body()))
+
+		r = prepareGetRequest(ctx, cnrID.EncodeToString(), objFileName)
+		hc.Handler().DownloadByAddressOrBucketName(r)
+		require.Equal(t, content, string(r.Response.Body()))
 	})
 
 	t.Run("head", func(t *testing.T) {
@@ -276,6 +287,16 @@ func TestBasic(t *testing.T) {
 		hc.Handler().HeadByAddressOrBucketName(r)
 		require.Equal(t, putRes.ObjectID, string(r.Response.Header.Peek(hdrObjectID)))
 		require.Equal(t, putRes.ContainerID, string(r.Response.Header.Peek(hdrContainerID)))
+
+		r = prepareGetRequest(ctx, cnrID.EncodeToString(), objFilePath)
+		hc.Handler().HeadByAddressOrBucketName(r)
+		require.Equal(t, putRes.ObjectID, string(r.Response.Header.Peek(hdrObjectID)))
+		require.Equal(t, putRes.ContainerID, string(r.Response.Header.Peek(hdrContainerID)))
+
+		r = prepareGetRequest(ctx, cnrID.EncodeToString(), objFileName)
+		hc.Handler().HeadByAddressOrBucketName(r)
+		require.Equal(t, putRes.ObjectID, string(r.Response.Header.Peek(hdrObjectID)))
+		require.Equal(t, putRes.ContainerID, string(r.Response.Header.Peek(hdrContainerID)))
 	})
 
 	t.Run("get by attribute", func(t *testing.T) {
@@ -285,11 +306,11 @@ func TestBasic(t *testing.T) {
 
 		r = prepareGetByAttributeRequest(ctx, bktName, attrFileName, objFilePath)
 		hc.Handler().DownloadByAttribute(r)
-		require.Equal(t, content, string(r.Response.Body()))
+		require.Equal(t, fasthttp.StatusNotFound, r.Response.StatusCode())
 
 		r = prepareGetByAttributeRequest(ctx, bktName, attrFilePath, objFileName)
 		hc.Handler().DownloadByAttribute(r)
-		require.Equal(t, content, string(r.Response.Body()))
+		require.Equal(t, fasthttp.StatusNotFound, r.Response.StatusCode())
 	})
 
 	t.Run("head by attribute", func(t *testing.T) {
@@ -300,13 +321,11 @@ func TestBasic(t *testing.T) {
 
 		r = prepareGetByAttributeRequest(ctx, bktName, attrFileName, objFilePath)
 		hc.Handler().HeadByAttribute(r)
-		require.Equal(t, putRes.ObjectID, string(r.Response.Header.Peek(hdrObjectID)))
-		require.Equal(t, putRes.ContainerID, string(r.Response.Header.Peek(hdrContainerID)))
+		require.Equal(t, fasthttp.StatusNotFound, r.Response.StatusCode())
 
 		r = prepareGetByAttributeRequest(ctx, bktName, attrFilePath, objFileName)
 		hc.Handler().HeadByAttribute(r)
-		require.Equal(t, putRes.ObjectID, string(r.Response.Header.Peek(hdrObjectID)))
-		require.Equal(t, putRes.ContainerID, string(r.Response.Header.Peek(hdrContainerID)))
+		require.Equal(t, fasthttp.StatusNotFound, r.Response.StatusCode())
 	})
 
 	t.Run("zip", func(t *testing.T) {
@@ -330,101 +349,187 @@ func TestBasic(t *testing.T) {
 	})
 }
 
-func TestFindObjectByAttribute(t *testing.T) {
+func prepareHandlerAndBucket(t *testing.T) (*handlerContext, cid.ID) {
 	hc := prepareHandlerContext(t)
-	hc.cfg.additionalFilenameSearch = true
 
 	bktName := "bucket"
 	cnrID, cnr, err := hc.prepareContainer(bktName, acl.PublicRWExtended)
 	require.NoError(t, err)
 	hc.frostfs.SetContainer(cnrID, cnr)
 
-	ctx := context.Background()
-	ctx = middleware.SetNamespace(ctx, "")
+	return hc, cnrID
+}
 
-	content := "hello"
-	r, err := prepareUploadRequest(ctx, cnrID.EncodeToString(), content)
-	require.NoError(t, err)
+func TestGetObjectWithFallback(t *testing.T) {
+	ctx := middleware.SetNamespace(context.Background(), "")
 
-	hc.Handler().Upload(r)
-	require.Equal(t, r.Response.StatusCode(), http.StatusOK)
+	t.Run("by oid", func(t *testing.T) {
+		hc, cnrID := prepareHandlerAndBucket(t)
 
-	var putRes putResponse
-	err = json.Unmarshal(r.Response.Body(), &putRes)
-	require.NoError(t, err)
+		obj1ID := oidtest.ID()
+		obj1 := object.New()
+		obj1.SetID(obj1ID)
+		obj1.SetPayload([]byte("obj1"))
+		hc.frostfs.objects[cnrID.String()+"/"+obj1ID.String()] = obj1
 
-	testAttrVal1 := "/folder/cat.jpg"
-	testAttrVal2 := "cat.jpg"
-	testAttrVal3 := "test-attr-val3"
+		r := prepareGetRequest(ctx, cnrID.EncodeToString(), obj1ID.String())
+		hc.Handler().DownloadByAddressOrBucketName(r)
+		require.Equal(t, string(obj1.Payload()), string(r.Response.Body()))
+	})
 
-	for _, tc := range []struct {
-		name             string
-		firstAttr        object.Attribute
-		secondAttr       object.Attribute
-		reqAttrKey       string
-		reqAttrValue     string
-		err              string
-		additionalSearch bool
-	}{
-		{
-			name:             "success search by FileName",
-			firstAttr:        prepareObjectAttributes(attrFilePath, testAttrVal1),
-			secondAttr:       prepareObjectAttributes(attrFileName, testAttrVal2),
-			reqAttrKey:       attrFileName,
-			reqAttrValue:     testAttrVal2,
-			additionalSearch: false,
-		},
-		{
-			name:             "failed search by FileName",
-			firstAttr:        prepareObjectAttributes(attrFilePath, testAttrVal1),
-			secondAttr:       prepareObjectAttributes(attrFileName, testAttrVal2),
-			reqAttrKey:       attrFileName,
-			reqAttrValue:     testAttrVal3,
-			err:              "not found",
-			additionalSearch: false,
-		},
-		{
-			name:             "success search by FilePath (with additional search)",
-			firstAttr:        prepareObjectAttributes(attrFilePath, testAttrVal1),
-			secondAttr:       prepareObjectAttributes(attrFileName, testAttrVal2),
-			reqAttrKey:       attrFilePath,
-			reqAttrValue:     testAttrVal2,
-			additionalSearch: true,
-		},
-		{
-			name:             "failed by FilePath (with additional search)",
-			firstAttr:        prepareObjectAttributes(attrFilePath, testAttrVal1),
-			secondAttr:       prepareObjectAttributes(attrFileName, testAttrVal2),
-			reqAttrKey:       attrFilePath,
-			reqAttrValue:     testAttrVal3,
-			err:              "not found",
-			additionalSearch: true,
-		},
-		{
-			name:             "success search by FilePath with leading slash (with additional search)",
-			firstAttr:        prepareObjectAttributes(attrFilePath, testAttrVal1),
-			secondAttr:       prepareObjectAttributes(attrFileName, testAttrVal2),
-			reqAttrKey:       attrFilePath,
-			reqAttrValue:     "/cat.jpg",
-			additionalSearch: true,
-		},
-	} {
-		t.Run(tc.name, func(t *testing.T) {
-			obj := hc.frostfs.objects[putRes.ContainerID+"/"+putRes.ObjectID]
-			obj.SetAttributes(tc.firstAttr, tc.secondAttr)
-			hc.cfg.additionalFilenameSearch = tc.additionalSearch
+	t.Run("by filepath as it is", func(t *testing.T) {
+		hc, cnrID := prepareHandlerAndBucket(t)
 
-			objID, err := hc.Handler().findObjectByAttribute(ctx, cnrID, tc.reqAttrKey, tc.reqAttrValue)
-			if tc.err != "" {
-				require.Error(t, err)
-				require.Contains(t, err.Error(), tc.err)
-				return
-			}
+		obj1ID := oidtest.ID()
+		obj1 := object.New()
+		obj1.SetID(obj1ID)
+		obj1.SetPayload([]byte("obj1"))
+		obj1.SetAttributes(prepareObjectAttributes(object.AttributeFilePath, "filepath/obj1"))
+		hc.frostfs.objects[cnrID.String()+"/"+obj1ID.String()] = obj1
 
-			require.NoError(t, err)
-			require.Equal(t, putRes.ObjectID, objID.EncodeToString())
-		})
-	}
+		obj2ID := oidtest.ID()
+		obj2 := object.New()
+		obj2.SetID(obj2ID)
+		obj2.SetPayload([]byte("obj2"))
+		obj2.SetAttributes(prepareObjectAttributes(object.AttributeFilePath, "/filepath/obj2"))
+		hc.frostfs.objects[cnrID.String()+"/"+obj2ID.String()] = obj2
+
+		r := prepareGetRequest(ctx, cnrID.EncodeToString(), "filepath/obj1")
+		hc.Handler().DownloadByAddressOrBucketName(r)
+		require.Equal(t, string(obj1.Payload()), string(r.Response.Body()))
+
+		r = prepareGetRequest(ctx, cnrID.EncodeToString(), "/filepath/obj2")
+		hc.Handler().DownloadByAddressOrBucketName(r)
+		require.Equal(t, string(obj2.Payload()), string(r.Response.Body()))
+	})
+
+	t.Run("by filepath slash fallback", func(t *testing.T) {
+		hc, cnrID := prepareHandlerAndBucket(t)
+
+		obj1ID := oidtest.ID()
+		obj1 := object.New()
+		obj1.SetID(obj1ID)
+		obj1.SetPayload([]byte("obj1"))
+		obj1.SetAttributes(prepareObjectAttributes(object.AttributeFilePath, "filepath/obj1"))
+		hc.frostfs.objects[cnrID.String()+"/"+obj1ID.String()] = obj1
+
+		r := prepareGetRequest(ctx, cnrID.EncodeToString(), "/filepath/obj1")
+		hc.Handler().DownloadByAddressOrBucketName(r)
+		require.Equal(t, fasthttp.StatusNotFound, r.Response.StatusCode())
+
+		hc.cfg.additionalSlashSearch = true
+
+		r = prepareGetRequest(ctx, cnrID.EncodeToString(), "/filepath/obj1")
+		hc.Handler().DownloadByAddressOrBucketName(r)
+		require.Equal(t, string(obj1.Payload()), string(r.Response.Body()))
+	})
+
+	t.Run("by filename fallback", func(t *testing.T) {
+		hc, cnrID := prepareHandlerAndBucket(t)
+
+		obj1ID := oidtest.ID()
+		obj1 := object.New()
+		obj1.SetID(obj1ID)
+		obj1.SetPayload([]byte("obj1"))
+		obj1.SetAttributes(prepareObjectAttributes(object.AttributeFileName, "filename/obj1"))
+		hc.frostfs.objects[cnrID.String()+"/"+obj1ID.String()] = obj1
+
+		r := prepareGetRequest(ctx, cnrID.EncodeToString(), "filename/obj1")
+		hc.Handler().DownloadByAddressOrBucketName(r)
+		require.Equal(t, fasthttp.StatusNotFound, r.Response.StatusCode())
+
+		hc.cfg.additionalFilenameSearch = true
+
+		r = prepareGetRequest(ctx, cnrID.EncodeToString(), "filename/obj1")
+		hc.Handler().DownloadByAddressOrBucketName(r)
+		require.Equal(t, string(obj1.Payload()), string(r.Response.Body()))
+	})
+
+	t.Run("by filename and slash fallback", func(t *testing.T) {
+		hc, cnrID := prepareHandlerAndBucket(t)
+
+		obj1ID := oidtest.ID()
+		obj1 := object.New()
+		obj1.SetID(obj1ID)
+		obj1.SetPayload([]byte("obj1"))
+		obj1.SetAttributes(prepareObjectAttributes(object.AttributeFileName, "filename/obj1"))
+		hc.frostfs.objects[cnrID.String()+"/"+obj1ID.String()] = obj1
+
+		r := prepareGetRequest(ctx, cnrID.EncodeToString(), "/filename/obj1")
+		hc.Handler().DownloadByAddressOrBucketName(r)
+		require.Equal(t, fasthttp.StatusNotFound, r.Response.StatusCode())
+
+		hc.cfg.additionalFilenameSearch = true
+
+		r = prepareGetRequest(ctx, cnrID.EncodeToString(), "/filename/obj1")
+		hc.Handler().DownloadByAddressOrBucketName(r)
+		require.Equal(t, fasthttp.StatusNotFound, r.Response.StatusCode())
+
+		hc.cfg.additionalSlashSearch = true
+
+		r = prepareGetRequest(ctx, cnrID.EncodeToString(), "/filename/obj1")
+		hc.Handler().DownloadByAddressOrBucketName(r)
+		require.Equal(t, string(obj1.Payload()), string(r.Response.Body()))
+	})
+
+	t.Run("index fallback", func(t *testing.T) {
+		hc, cnrID := prepareHandlerAndBucket(t)
+
+		obj1ID := oidtest.ID()
+		obj1 := object.New()
+		obj1.SetID(obj1ID)
+		obj1.SetPayload([]byte("obj1"))
+		obj1.SetAttributes(prepareObjectAttributes(object.AttributeFilePath, "filepath/index.html"))
+		hc.frostfs.objects[cnrID.String()+"/"+obj1ID.String()] = obj1
+
+		r := prepareGetRequest(ctx, cnrID.EncodeToString(), "filepath/")
+		hc.Handler().DownloadByAddressOrBucketName(r)
+		require.Equal(t, fasthttp.StatusNotFound, r.Response.StatusCode())
+
+		r = prepareGetRequest(ctx, cnrID.EncodeToString(), "filepath")
+		hc.Handler().DownloadByAddressOrBucketName(r)
+		require.Equal(t, fasthttp.StatusNotFound, r.Response.StatusCode())
+
+		hc.cfg.indexEnabled = true
+
+		r = prepareGetRequest(ctx, cnrID.EncodeToString(), "filepath")
+		hc.Handler().DownloadByAddressOrBucketName(r)
+		require.Equal(t, string(obj1.Payload()), string(r.Response.Body()))
+
+		r = prepareGetRequest(ctx, cnrID.EncodeToString(), "filepath/")
+		hc.Handler().DownloadByAddressOrBucketName(r)
+		require.Equal(t, string(obj1.Payload()), string(r.Response.Body()))
+	})
+
+	t.Run("index filename fallback", func(t *testing.T) {
+		hc, cnrID := prepareHandlerAndBucket(t)
+
+		obj1ID := oidtest.ID()
+		obj1 := object.New()
+		obj1.SetID(obj1ID)
+		obj1.SetPayload([]byte("obj1"))
+		obj1.SetAttributes(prepareObjectAttributes(object.AttributeFileName, "filename/index.html"))
+		hc.frostfs.objects[cnrID.String()+"/"+obj1ID.String()] = obj1
+
+		r := prepareGetRequest(ctx, cnrID.EncodeToString(), "filename/")
+		hc.Handler().DownloadByAddressOrBucketName(r)
+		require.Equal(t, fasthttp.StatusNotFound, r.Response.StatusCode())
+
+		r = prepareGetRequest(ctx, cnrID.EncodeToString(), "filename")
+		hc.Handler().DownloadByAddressOrBucketName(r)
+		require.Equal(t, fasthttp.StatusNotFound, r.Response.StatusCode())
+
+		hc.cfg.indexEnabled = true
+		hc.cfg.additionalFilenameSearch = true
+
+		r = prepareGetRequest(ctx, cnrID.EncodeToString(), "filename")
+		hc.Handler().DownloadByAddressOrBucketName(r)
+		require.Equal(t, string(obj1.Payload()), string(r.Response.Body()))
+
+		r = prepareGetRequest(ctx, cnrID.EncodeToString(), "filename/")
+		hc.Handler().DownloadByAddressOrBucketName(r)
+		require.Equal(t, string(obj1.Payload()), string(r.Response.Body()))
+	})
 }
 
 func prepareUploadRequest(ctx context.Context, bucket, content string) (*fasthttp.RequestCtx, error) {
diff --git a/internal/handler/head.go b/internal/handler/head.go
index e130124..e6d9a30 100644
--- a/internal/handler/head.go
+++ b/internal/handler/head.go
@@ -175,15 +175,6 @@ func (h *Handler) HeadByAddressOrBucketName(req *fasthttp.RequestCtx) {
 			Middleware{Func: h.byAttributeSearchMiddleware(h.headObject, object.AttributeFileName, indexFormer), Enabled: fileNameFallbackEnabled && indexPageEnabled},
 		)
 	}
-
-	var objID oid.ID
-	if checkS3Err == nil {
-		h.byS3Path(ctx, req, bktInfo, oidParam, h.headObject)
-	} else if err = objID.DecodeString(oidParam); err == nil {
-		h.byNativeAddress(ctx, req, bktInfo.CID, objID, h.headObject)
-	} else {
-		h.logAndSendError(ctx, req, logs.InvalidOIDParam, err)
-	}
 }
 
 // HeadByAttribute handles attribute-based head requests.