diff --git a/core/base/mergeTreeClustering/MergeTreeBase.h b/core/base/mergeTreeClustering/MergeTreeBase.h
index 2e49b35000..64a1b0b49f 100644
--- a/core/base/mergeTreeClustering/MergeTreeBase.h
+++ b/core/base/mergeTreeClustering/MergeTreeBase.h
@@ -40,6 +40,7 @@ namespace ttk {
     int wassersteinPower_ = 2;
     bool normalizedWasserstein_ = true;
     bool keepSubtree_ = false;
+    double nonMatchingWeight_ = 1.0;
 
     bool distanceSquaredRoot_ = true; // squared root
     bool useFullMerge_ = false;
@@ -122,6 +123,10 @@ namespace ttk {
       keepSubtree_ = keepSubtree;
     }
 
+    void setNonMatchingWeight(double weight) {
+      nonMatchingWeight_ = weight;
+    }
+
     void setBarycenterMergeTree(bool imt) {
       barycenterMergeTree_ = imt;
     }
@@ -1128,6 +1133,7 @@ namespace ttk {
       // Divide cost by two if not branch decomposition and not merged
       /*if(! branchDecomposition_ and ! tree->isNodeMerged(nodeId))
         cost /= 2;*/
+      cost *= nonMatchingWeight_;
 
       return cost;
     }
diff --git a/core/vtk/ttkMergeTreeClustering/ttkMergeTreeClustering.cpp b/core/vtk/ttkMergeTreeClustering/ttkMergeTreeClustering.cpp
index aa6b19949a..d0384c9dbe 100644
--- a/core/vtk/ttkMergeTreeClustering/ttkMergeTreeClustering.cpp
+++ b/core/vtk/ttkMergeTreeClustering/ttkMergeTreeClustering.cpp
@@ -265,6 +265,7 @@ int ttkMergeTreeClustering::runCompute(
     mergeTreeDistance.setDeleteMultiPersPairs(DeleteMultiPersPairs);
     mergeTreeDistance.setEpsilon1UseFarthestSaddle(Epsilon1UseFarthestSaddle);
     mergeTreeDistance.setIsPersistenceDiagram(IsPersistenceDiagram);
+    mergeTreeDistance.setNonMatchingWeight(NonMatchingWeight);
     mergeTreeDistance.setThreadNumber(this->threadNumber_);
     mergeTreeDistance.setDebugLevel(this->debugLevel_);
 
diff --git a/core/vtk/ttkMergeTreeClustering/ttkMergeTreeClustering.h b/core/vtk/ttkMergeTreeClustering/ttkMergeTreeClustering.h
index 10378862d4..6496db0504 100644
--- a/core/vtk/ttkMergeTreeClustering/ttkMergeTreeClustering.h
+++ b/core/vtk/ttkMergeTreeClustering/ttkMergeTreeClustering.h
@@ -96,6 +96,7 @@ class TTKMERGETREECLUSTERING_EXPORT ttkMergeTreeClustering
   int pathMetric = 0;
   int branchMetric = 0;
   int baseModule = 0;
+  double NonMatchingWeight = 1.0;
 
   // Output Options
   bool OutputTrees = true;
@@ -341,6 +342,13 @@ class TTKMERGETREECLUSTERING_EXPORT ttkMergeTreeClustering
     Modified();
   }
 
+  void SetNonMatchingWeight(double weight) {
+    NonMatchingWeight = weight;
+    Modified();
+    resetDataVisualization();
+  }
+  vtkGetMacro(NonMatchingWeight, double);
+
   // Output Options
   vtkSetMacro(BarycenterPositionAlpha, bool);
   vtkGetMacro(BarycenterPositionAlpha, bool);
diff --git a/paraview/xmls/MergeTreeClustering.xml b/paraview/xmls/MergeTreeClustering.xml
index 2057ad241a..b9c688e1ef 100644
--- a/paraview/xmls/MergeTreeClustering.xml
+++ b/paraview/xmls/MergeTreeClustering.xml
@@ -305,6 +305,24 @@ Online examples:
                   <DoubleRangeDomain name="range" min="0" max="1" />
                 </DoubleVectorProperty>
                 
+                <DoubleVectorProperty
+                name="NonMatchingWeight"
+                command="SetNonMatchingWeight"
+                label="Non Matching Weight"
+                number_of_elements="1"
+                default_values="1"
+                panel_visibility="advanced">
+                  <Hints>
+                  <PropertyWidgetDecorator type="GenericDecorator"
+                                           mode="visibility"
+                                           property="ComputeBarycenter"
+                                           value="0" />
+                  </Hints>
+                  <Documentation>
+                    Weight given to the insertion and deletion costs in the distance computation.
+                  </Documentation>
+                </DoubleVectorProperty>
+                
                 <!-- Input options -->
                 <!-- TODO <IntVectorProperty
                 name="UseMinMaxPair"
@@ -461,6 +479,7 @@ Online examples:
               <Property name="Deterministic"/>
               <Property name="Alpha"/>
               <Property name="JoinSplitMixtureCoefficient"/>
+              <Property name="NonMatchingWeight"/>
               <!-- <Property name="UseMinMaxPair"/> -->
             </PropertyGroup>
             ${MERGE_TREE_PREPROCESS_WIDGETS}