diff --git a/modules/dnn/src/tflite/tflite_importer.cpp b/modules/dnn/src/tflite/tflite_importer.cpp
index e44dd669270b..dd74d6ead0e7 100644
--- a/modules/dnn/src/tflite/tflite_importer.cpp
+++ b/modules/dnn/src/tflite/tflite_importer.cpp
@@ -86,7 +86,7 @@ class TFLiteImporter {
     int addReshapeLayer(const std::vector<int>& shape, int axis, int num_axes,
                         const std::string& name, const std::pair<int, int>& inpId, int dtype, int inpTensorId);
     int addFlattenLayer(int axis, int end_axis, const std::string& name, const std::pair<int, int>& inpId, int dtype, int outTensorId);
-    int addConstLayer(const Mat& data, const std::string& name);
+    void addConstLayer(const Mat& data, int tensorIdx);
 
     inline bool isInt8(const Operator& op);
     inline void getQuantParams(const Operator& op, float& inpScale, int& inpZero, float& outScale, int& outZero);
@@ -488,11 +488,13 @@ void TFLiteImporter::parseConvolution(const Operator& op, const std::string& opc
     layerParams.type = "Convolution";
 
     int inpId = op.inputs()->Get(0);
+    bool additionalPreLayer = false;
     if (layouts[inpId] == DNN_LAYOUT_UNKNOWN && modelTensors->Get(inpId)->shape()->size() == 4)
     {
         int permId = addPermuteLayer({0, 3, 1, 2}, layerParams.name + "/permute_input", layerIds[inpId], isInt8(op) ? CV_8S : CV_32F, op.inputs()->Get(0));  // NHWC -> NCHW
         layerIds[inpId] = std::make_pair(permId, 0);
         layouts[op.outputs()->Get(0)] = DNN_LAYOUT_NHWC;
+        additionalPreLayer = true;
     }
 
     auto options = reinterpret_cast<const Conv2DOptions*>(op.builtin_options());
@@ -554,7 +556,7 @@ void TFLiteImporter::parseConvolution(const Operator& op, const std::string& opc
 
     std::string fusedActivationType = EnumNameActivationFunctionType(options->fused_activation_function());
     bool haveFusedActivation = fusedActivationType != "NONE";
-    addLayer(layerParams, op, false, haveFusedActivation);
+    addLayer(layerParams, op, additionalPreLayer, haveFusedActivation);
     parseFusedActivation(op, options->fused_activation_function());
 }
 
@@ -720,27 +722,33 @@ void TFLiteImporter::parseEltwise(const Operator& op, const std::string& opcode,
         if (layouts[op.inputs()->Get(0)] == DNN_LAYOUT_NHWC && blob.dims == 1) {
             blob = blob.reshape(1, {1, (int)blob.total(), 1, 1});
         }
-        int constId = addConstLayer(blob, modelTensors->Get(idx)->name()->str());
-        layerIds[idx] = std::make_pair(constId, 0);
+        addConstLayer(blob, idx);
     }
 
 
     std::string fusedActivationType = EnumNameActivationFunctionType(activ);
     bool haveFusedActivation = fusedActivationType != "NONE";
-    addLayer(layerParams, op, false, haveFusedActivation);
+    addLayer(layerParams, op, false, haveFusedActivation || opcode == "SQUARED_DIFFERENCE" || opcode == "RSQRT");
     parseFusedActivation(op, activ);
 
-    // Layers that split on multiple operations
-    if (opcode == "SQUARED_DIFFERENCE") {
-        LayerParams lp;
-        lp.set("power", 2);
-        int id = dstNet.addLayerToPrev(layerParams.name + "/square", "Power", isOpInt8 ? CV_8S : CV_32F, lp);
-        layerIds[op.outputs()->Get(0)] = std::make_pair(id, 0);
-    }
-    else if (opcode == "RSQRT") {
+    if (opcode == "SQUARED_DIFFERENCE" || opcode == "RSQRT") {
+        if (haveFusedActivation)
+            CV_LOG_WARNING(NULL, format("%s with fused activation on new engine is not tested", opcode.c_str()));
         LayerParams lp;
-        int id = dstNet.addLayerToPrev(layerParams.name + "/inv", "Reciprocal", isOpInt8 ? CV_8S : CV_32F, lp);
-        layerIds[op.outputs()->Get(0)] = std::make_pair(id, 0);
+        if (opcode == "RSQRT")
+            lp.type = "Reciprocal";
+        else {
+            lp.type = "Power";
+            lp.set("power", 2);
+        }
+        if (newEngine) {
+            std::string tensorName = modelTensors->Get(op.outputs()->Get(0))->name()->str();
+            addLayer(lp, {tensorName + "_additional_post_layer"}, {tensorName});
+            layerIds[op.outputs()->Get(0)] = std::make_pair(-1, -1);
+        } else {
+            int id = dstNet.addLayerToPrev(layerParams.name + "/post", lp.type, isOpInt8 ? CV_8S : CV_32F, lp);
+            layerIds[op.outputs()->Get(0)] = std::make_pair(id, 0);
+        }
     }
 }
 
@@ -866,8 +874,7 @@ void TFLiteImporter::parseConcat(const Operator& op, const std::string& opcode,
             transposeND(blob, {0, 3, 1, 2}, nchwBlob);
             blob = nchwBlob;
         }
-        int constId = addConstLayer(blob, modelTensors->Get(idx)->name()->str());
-        layerIds[idx] = std::make_pair(constId, 0);
+        addConstLayer(blob, idx);
     }
 
     std::string fusedActivationType = EnumNameActivationFunctionType(options->fused_activation_function());
@@ -1079,11 +1086,23 @@ int TFLiteImporter::addFlattenLayer(int axis, int end_axis, const std::string& n
     }
 }
 
-int TFLiteImporter::addConstLayer(const Mat& blob, const std::string& name)
+void TFLiteImporter::addConstLayer(const Mat& blob, int tensorIdx)
 {
+    const std::string& name = modelTensors->Get(tensorIdx)->name()->str();
     LayerParams lp;
     lp.blobs.push_back(blob.u ? blob : blob.clone());  // some tensors are owned by OpenCV
-    return dstNet.addLayer(name, "Const", lp);
+    if (newEngine)
+    {
+        lp.type = "Const";
+        lp.name = name;
+        addLayer(lp, {}, {name});
+        layerIds[tensorIdx] = std::make_pair(-1, -1);
+    }
+    else
+    {
+        int constId = dstNet.addLayer(name, "Const", lp);
+        layerIds[tensorIdx] = std::make_pair(constId, 0);
+    }
 }
 
 void TFLiteImporter::parseDeconvolution(const Operator& op, const std::string& opcode, LayerParams& layerParams) {
@@ -1218,21 +1237,31 @@ void TFLiteImporter::parseStridedSlice(const Operator& op, const std::string& op
             lastShrinkAxis = axis;
     }
     std::string layerName = layerParams.name;
-    if (lastShrinkAxis != -1)
+    if (!newEngine && lastShrinkAxis != -1)
     {
         layerParams.name += "/slice";
     }
 
-    addLayer(layerParams, op);
+    addLayer(layerParams, op, false, lastShrinkAxis != -1);
 
     for (int axis = 0; axis < num; ++axis)
     {
         if (!(shrinkMask & (1 << axis)))
             continue;
-        std::string name = (axis == lastShrinkAxis) ? layerName : format("%s/shrink_axis_%d", layerName.c_str(), axis);
-        int layerId = addFlattenLayer(axis, axis + 1, name,
-            layerIds[op.outputs()->Get(0)], isInt8(op) ? CV_8S : CV_32F, op.inputs()->Get(0));
-        layerIds[op.inputs()->Get(0)] = std::make_pair(layerId, 0);
+        if (newEngine)
+        {
+            if (axis != lastShrinkAxis)
+                CV_LOG_WARNING(NULL, "StridedSlice with multiple axes shrink in new engine is not tested");
+            addFlattenLayer(axis, axis + 1, layerName,
+                layerIds[op.outputs()->Get(0)], isInt8(op) ? CV_8S : CV_32F, op.outputs()->Get(0));
+        }
+        else
+        {
+            std::string name = (axis == lastShrinkAxis) ? layerName : format("%s/shrink_axis_%d", layerName.c_str(), axis);
+            int layerId = addFlattenLayer(axis, axis + 1, name,
+                layerIds[op.outputs()->Get(0)], isInt8(op) ? CV_8S : CV_32F, op.inputs()->Get(0));
+            layerIds[op.inputs()->Get(0)] = std::make_pair(layerId, 0);
+        }
     }
 }
 
@@ -1328,22 +1357,7 @@ void TFLiteImporter::parseDetectionPostProcess(const Operator& op, const std::st
         layerParams.set("variance_encoded_in_target", true);
     }
 
-    LayerParams priorsLP;
-    priorsLP.name = layerParams.name + "/priors";
-    priorsLP.type = "Const";
-    priorsLP.blobs.resize(1, priors);
-
-    if (newEngine)
-    {
-        std::string outTensorName = modelTensors->Get(op.inputs()->Get(2))->name()->str();
-        addLayer(priorsLP, {}, {outTensorName});
-        layerIds[op.inputs()->Get(2)] = std::make_pair(-1, -1);
-    }
-    else
-    {
-        int priorsId = dstNet.addLayer(priorsLP.name, priorsLP.type, priorsLP);
-        layerIds[op.inputs()->Get(2)] = std::make_pair(priorsId, 0);
-    }
+    addConstLayer(priors, op.inputs()->Get(2));
     addLayer(layerParams, op);
 }
 
diff --git a/modules/dnn/test/test_tflite_importer.cpp b/modules/dnn/test/test_tflite_importer.cpp
index 52e5ecef275e..b4e89ee46cdd 100644
--- a/modules/dnn/test/test_tflite_importer.cpp
+++ b/modules/dnn/test/test_tflite_importer.cpp
@@ -283,7 +283,7 @@ TEST_P(Test_TFLite, StridedSlice) {
     testLayer("strided_slice");
 }
 
-TEST_P(Test_TFLite, DISABLED_face_blendshapes)
+TEST_P(Test_TFLite, face_blendshapes)
 {
     Mat inp = blobFromNPY(findDataFile("dnn/tflite/face_blendshapes_inp.npy"));
     testModel("face_blendshapes", inp);

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