diff --git a/src/fvMeshMovers/multiValveEngine/movingObject.C b/src/fvMeshMovers/multiValveEngine/movingObject.C
index 8da4dc20df..4d72c02b46 100644
--- a/src/fvMeshMovers/multiValveEngine/movingObject.C
+++ b/src/fvMeshMovers/multiValveEngine/movingObject.C
@@ -211,6 +211,64 @@ Foam::fvMeshMovers::multiValveEngine::movingObject::movingPointZones() const
 }
 
 
+Foam::labelHashSet
+Foam::fvMeshMovers::multiValveEngine::movingObject::staticPointZones() const
+{
+    labelHashSet staticPointZones;
+
+    if (frozenPointZones_.size())
+    {
+        forAll(frozenPointZones_, i)
+        {
+            const labelList indices
+            (
+                meshMover_.mesh().pointZones().findIndices(frozenPointZones_[i])
+            );
+
+            if (indices.size())
+            {
+                staticPointZones.insert(indices);
+                Info<< "    pointZone " << frozenPointZones_[i]
+                    << " is frozen (stationary)" << endl;
+            }
+            else
+            {
+                Info<< "    frozenZone " << frozenPointZones_[i]
+                    << " not found in pointZones" << endl;
+            }
+        }
+    }
+
+    if (meshMover_.frozenPointZones_.size())
+    {
+        forAll(meshMover_.frozenPointZones_, i)
+        {
+            const labelList indices
+            (
+                meshMover_.mesh().pointZones().findIndices
+                (
+                    meshMover_.frozenPointZones_[i]
+                )
+            );
+
+            if (indices.size())
+            {
+                staticPointZones.insert(indices);
+                Info<< "    pointZone " << meshMover_.frozenPointZones_[i]
+                    << " is frozen (stationary)" << endl;
+            }
+            else
+            {
+                Info<< "    frozenZone " << meshMover_.frozenPointZones_[i]
+                    << " not found in pointZones" << endl;
+            }
+        }
+    }
+
+    return staticPointZones;
+}
+
+
 // * * * * * * * * * * * * * * * * Constructors  * * * * * * * * * * * * * * //
 
 Foam::fvMeshMovers::multiValveEngine::movingObject::movingObject
@@ -241,6 +299,10 @@ Foam::fvMeshMovers::multiValveEngine::movingObject::movingObject
     (
         dict.lookupOrDefault("movingZones", wordReList::null())
     ),
+    frozenPointZones_
+    (
+        dict.lookupOrDefault("frozenZones", wordReList::null())
+    ),
     scale_
     (
         IOobject
diff --git a/src/fvMeshMovers/multiValveEngine/multiValveEngine.C b/src/fvMeshMovers/multiValveEngine/multiValveEngine.C
index b73d55bcb6..0f6efb4a10 100644
--- a/src/fvMeshMovers/multiValveEngine/multiValveEngine.C
+++ b/src/fvMeshMovers/multiValveEngine/multiValveEngine.C
@@ -95,38 +95,6 @@ Foam::labelHashSet Foam::fvMeshMovers::multiValveEngine::findStaticPatchSet()
 }
 
 
-Foam::labelHashSet
-Foam::fvMeshMovers::multiValveEngine::staticPointZones() const
-{
-    labelHashSet staticPointZones;
-
-    if (frozenPointZones_.size())
-    {
-        forAll(frozenPointZones_, i)
-        {
-            const labelList indices
-            (
-                mesh().pointZones().findIndices(frozenPointZones_[i])
-            );
-
-            if (indices.size())
-            {
-                staticPointZones.insert(indices);
-                Info<< "    pointZone " << frozenPointZones_[i]
-                    << " is frozen (stationary)" << endl;
-            }
-            else
-            {
-                Info<< "    frozenZone " << frozenPointZones_[i]
-                    << " not found in pointZones" << endl;
-            }
-        }
-    }
-
-    return staticPointZones;
-}
-
-
 // * * * * * * * * * * * * * * * * Constructors  * * * * * * * * * * * * * * //
 
 Foam::fvMeshMovers::multiValveEngine::multiValveEngine(fvMesh& mesh)
diff --git a/src/fvMeshMovers/multiValveEngine/multiValveEngine.H b/src/fvMeshMovers/multiValveEngine/multiValveEngine.H
index f1f1d5633a..134a9ebe4b 100644
--- a/src/fvMeshMovers/multiValveEngine/multiValveEngine.H
+++ b/src/fvMeshMovers/multiValveEngine/multiValveEngine.H
@@ -45,7 +45,7 @@ Description
       slide mesh nodes while piston is moving.
 
     - frozenZones: list of pointZones the points of which are frozen,
-      i.e. do not move.
+      i.e. do not move with respect to any moving object.
 
     - Run-time clearance estimation based on patch-to-patch distances printed.
 
@@ -67,6 +67,9 @@ Description
         - movingZones: list of pointZones the points of which move with the
           object.
 
+        - frozenZones: list of pointZones the points of which are frozen,
+          i.e. do not move with respect to this moving object.
+
         - maxMotionDistance: a distance away from the moving object
           after nodes are not allowed to move. (Default inf.)
 
@@ -152,6 +155,9 @@ Description
             // Move the points in the piston bowl with the piston
             movingZones         (pistonBowl);
 
+            // Freeze the points in the cylinder head
+            frozenZones         (cylinderHead);
+
             // Optional
             maxMotionDistance    1e30;
             movingFrozenLayerThickness  0;
@@ -295,6 +301,8 @@ public:
 
             wordReList movingPointZones_;
 
+            wordReList frozenPointZones_;
+
             //- Points to move when cell zone is supplied
             labelList pointIDs_;
 
@@ -344,6 +352,8 @@ public:
 
             labelHashSet movingPointZones() const;
 
+            labelHashSet staticPointZones() const;
+
 
     public:
 
@@ -551,8 +561,6 @@ private:
         //- Find and return the static patch set
         labelHashSet findStaticPatchSet();
 
-        labelHashSet staticPointZones() const;
-
 
 public:
 
diff --git a/src/fvMeshMovers/multiValveEngine/piston.C b/src/fvMeshMovers/multiValveEngine/piston.C
index ef76ddb992..21c213dd98 100644
--- a/src/fvMeshMovers/multiValveEngine/piston.C
+++ b/src/fvMeshMovers/multiValveEngine/piston.C
@@ -182,7 +182,7 @@ void Foam::fvMeshMovers::multiValveEngine::pistonObject::updatePoints
         (
             pMesh,
             staticPatchSet_,
-            meshMover_.staticPointZones(),
+            staticPointZones(),
             points,
             maxMotionDistance_
         );
diff --git a/src/fvMeshMovers/multiValveEngine/valve.C b/src/fvMeshMovers/multiValveEngine/valve.C
index 00577a3b64..353129071f 100644
--- a/src/fvMeshMovers/multiValveEngine/valve.C
+++ b/src/fvMeshMovers/multiValveEngine/valve.C
@@ -119,7 +119,7 @@ void Foam::fvMeshMovers::multiValveEngine::valveObject::updatePoints
             (
                 pMesh,
                 staticPatchSet_,
-                meshMover_.staticPointZones(),
+                staticPointZones(),
                 points,
                 maxMotionDistance_
             );
diff --git a/tutorials/XiFluid/kivaTest/constant/dynamicMeshDict b/tutorials/XiFluid/kivaTest/constant/dynamicMeshDict
index 3d319dadd1..1c94918bb6 100644
--- a/tutorials/XiFluid/kivaTest/constant/dynamicMeshDict
+++ b/tutorials/XiFluid/kivaTest/constant/dynamicMeshDict
@@ -24,9 +24,6 @@ mover
     slidingPatches      (liner);
     linerPatches        (liner);
 
-    // Freeze the points in the cylinder head
-    frozenZones         (cylinderHead);
-
     piston
     {
         patches             (piston);
@@ -43,6 +40,9 @@ mover
         // Move the points in the piston bowl with the piston
         movingZones         (pistonBowl);
 
+        // Freeze the points in the cylinder head
+        frozenZones         (cylinderHead);
+
         // There is no need to update the motion weights
         fractionalTravelInterval       1;
     }