diff --git a/tutorials/mesh/foamyHexMesh/Allrun b/tutorials/mesh/foamyHexMesh/Allrun
index 93da24214..89721a10a 100755
--- a/tutorials/mesh/foamyHexMesh/Allrun
+++ b/tutorials/mesh/foamyHexMesh/Allrun
@@ -8,25 +8,28 @@ cd ${0%/*} || exit 1    # Run from this directory
 # Source tutorial run functions
 . $WM_PROJECT_DIR/bin/tools/RunFunctions
 
-(
-    cd blob || exit
-    ./Allrun $*
-)
-(
-    cd simpleShapes || exit
-    ./Allrun $*
-)
-
-if ! isTest $@
+if [ -n "$FOAMY_HEX_MESH" ]
 then
     (
-        cd flange || exit
+        cd blob || exit
         ./Allrun $*
     )
     (
-        cd mixerVessel || exit
+        cd simpleShapes || exit
         ./Allrun $*
     )
+
+    if ! isTest $@
+    then
+        (
+            cd flange || exit
+            ./Allrun $*
+        )
+        (
+            cd mixerVessel || exit
+            ./Allrun $*
+        )
+    fi
 fi
 
 #------------------------------------------------------------------------------
diff --git a/tutorials/mesh/foamyQuadMesh/Allrun b/tutorials/mesh/foamyQuadMesh/Allrun
new file mode 100755
index 000000000..42625efa9
--- /dev/null
+++ b/tutorials/mesh/foamyQuadMesh/Allrun
@@ -0,0 +1,27 @@
+#!/bin/sh
+cd ${0%/*} || exit 1    # Run from this directory
+
+# Any cases that are links to solver test cases and are run when the Allrun
+# scripts of those solvers are run.  This script avoids meshing these cases
+# twice.
+
+# Source tutorial run functions
+. $WM_PROJECT_DIR/bin/tools/RunFunctions
+
+if [ -n "$FOAMY_HEX_MESH" ]
+then
+    (
+        cd jaggedBoundary || exit
+        ./Allrun $*
+    )
+    (
+        cd OpenCFD || exit
+        ./Allrun $*
+    )
+    (
+        cd square || exit
+        ./Allrun $*
+    )
+fi
+
+#------------------------------------------------------------------------------