diff --git a/applications/test/bitSet1/Test-bitSet1.C b/applications/test/bitSet1/Test-bitSet1.C
index 7077bcb371..2ed6f56d16 100644
--- a/applications/test/bitSet1/Test-bitSet1.C
+++ b/applications/test/bitSet1/Test-bitSet1.C
@@ -2,7 +2,7 @@
   =========                 |
   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
    \\    /   O peration     |
-    \\  /    A nd           | Copyright (C) 2018 OpenCFD Ltd.
+    \\  /    A nd           | Copyright (C) 2018-2019 OpenCFD Ltd.
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
 License
@@ -33,6 +33,7 @@ Description
 #include "boolList.H"
 #include "bitSet.H"
 #include "HashSet.H"
+#include "ListOps.H"
 #include "cpuTime.H"
 #include <vector>
 #include <unordered_set>
@@ -91,6 +92,9 @@ int main(int argc, char *argv[])
         set3b.unset(FixedList<label, 3>({ 1, 2, 3}));
 
         Info<<"bitSet unset(FixedList<label>): "; report(set3b, true);
+
+        Info<<"bits used: " << flatOutput(set3b.toc()) << nl;
+        Info<<"inverted:  " << flatOutput(invert(set3b)) << nl;
     }
 
     Info<< "End\n" << endl;
diff --git a/src/OpenFOAM/containers/Lists/ListOps/ListOps.C b/src/OpenFOAM/containers/Lists/ListOps/ListOps.C
index 5f6d2a04d5..5fd24ea4c2 100644
--- a/src/OpenFOAM/containers/Lists/ListOps/ListOps.C
+++ b/src/OpenFOAM/containers/Lists/ListOps/ListOps.C
@@ -38,10 +38,9 @@ Foam::labelList Foam::invert
 {
     labelList inverse(len, -1);
 
-    forAll(map, i)
+    label i = 0;
+    for (const label newIdx : map)
     {
-        const label newIdx = map[i];
-
         if (newIdx >= 0)
         {
             #ifdef FULLDEBUG
@@ -58,19 +57,57 @@ Foam::labelList Foam::invert
             {
                 FatalErrorInFunction
                     << "Map is not one-to-one. At index " << i
-                    << " element " << newIdx << " has already occurred before"
-                    << nl << "Please use invertOneToMany instead"
+                    << " element " << newIdx << " has already occurred\n"
+                    << "Please use invertOneToMany instead"
                     << abort(FatalError);
             }
 
             inverse[newIdx] = i;
         }
+
+        ++i;
     }
 
     return inverse;
 }
 
 
+Foam::labelList Foam::invert
+(
+    const label len,
+    const bitSet& map
+)
+{
+    labelList inverse(len, -1);
+
+    label i = 0;
+    for (const label newIdx : map)
+    {
+        #ifdef FULLDEBUG
+        if (newIdx >= len)
+        {
+            FatalErrorInFunction
+                << "Inverse location " << newIdx
+                << " is out of range. List has size " << len
+                << abort(FatalError);
+        }
+        #endif
+
+        inverse[newIdx] = i;
+
+        ++i;
+    }
+
+    return inverse;
+}
+
+
+Foam::labelList Foam::invert(const bitSet& map)
+{
+    return invert(map.size(), map);
+}
+
+
 Foam::labelListList Foam::invertOneToMany
 (
     const label len,
@@ -95,14 +132,15 @@ Foam::labelListList Foam::invertOneToMany
         sizes[i] = 0; // reset size counter
     }
 
-    forAll(map, i)
+    label i = 0;
+    for (const label newIdx : map)
     {
-        const label newIdx = map[i];
-
         if (newIdx >= 0)
         {
             inverse[newIdx][sizes[newIdx]++] = i;
         }
+
+        ++i;
     }
 
     return inverse;
diff --git a/src/OpenFOAM/containers/Lists/ListOps/ListOps.H b/src/OpenFOAM/containers/Lists/ListOps/ListOps.H
index 224a1c6223..4e257aee0b 100644
--- a/src/OpenFOAM/containers/Lists/ListOps/ListOps.H
+++ b/src/OpenFOAM/containers/Lists/ListOps/ListOps.H
@@ -334,9 +334,29 @@ void inplaceSubsetList
 );
 
 
-//- Invert one-to-one map. Unmapped elements will be -1.
+//- Create an inverse one-to-one mapping.
+//  \param len the output size
+//  \param map the unique indices to map, in a [0..len) range.
+//       Any negative indices are ignored.
+//
+//  \return the inverse mapping with -1 for unmapped elements.
 labelList invert(const label len, const labelUList& map);
 
+//- Create an inverse one-to-one mapping for all 'on' bits of the map.
+//  \param len the output size
+//  \param map the 'on' bits to use for the mapping indices.
+//      The last on bit shall be less than len.
+//
+//  \return the inverse mapping with -1 for unmapped elements.
+labelList invert(const label len, const bitSet& map);
+
+//- Create an inverse one-to-one mapping for all 'on' bits of the map.
+//  The output size is dictated by the map size.
+//  \param map the unique indices to map.
+//
+//  \return the inverse mapping with -1 for unmapped elements.
+labelList invert(const bitSet& map);
+
 //- Invert one-to-many map. Unmapped elements will be size 0.
 labelListList invertOneToMany(const label len, const labelUList& map);