diff --git a/applications/test/HashSet/Test-hashSet.C b/applications/test/HashSet/Test-hashSet.C
index 0b219f2e3d..55640829fb 100644
--- a/applications/test/HashSet/Test-hashSet.C
+++ b/applications/test/HashSet/Test-hashSet.C
@@ -197,8 +197,12 @@ int main(int argc, char *argv[])
         Info<< "setD has no 11" << endl;
     }
 
+    Info<< "setB : " << flatOutput(setB) << endl;
     Info<< "setD : " << flatOutput(setD) << endl;
 
+    setD -= setB;
+    Info<< "setD -= setB : " << flatOutput(setD) << endl;
+
     // This should not work (yet?)
     // setD[12] = true;
 
diff --git a/applications/test/HashTable/Test-hashTable.C b/applications/test/HashTable/Test-hashTable.C
index 31bff05b0f..173356b238 100644
--- a/applications/test/HashTable/Test-hashTable.C
+++ b/applications/test/HashTable/Test-hashTable.C
@@ -25,6 +25,7 @@ License
 
 #include "HashTable.H"
 #include "List.H"
+#include "FlatOutput.H"
 #include "IOstreams.H"
 #include "IStringStream.H"
 #include "OStringStream.H"
@@ -163,15 +164,15 @@ int main()
         << "\ntable2" << table2 << nl;
 
 
-    Info<< "\ntable3" << table3
-        << "\nclearStorage table3 ... ";
-    table3.clearStorage();
-    Info<< table3 << nl;
+    Info<< "\ntable3" << table2
+        << "\nclearStorage table2 ... ";
+    table2.clearStorage();
+    Info<< table2 << nl;
 
     table1 =
     {
-        {"aca", 3.0},
-        {"aaw", 6.0},
+        {"abc", 3.0},
+        {"def", 6.0},
         {"acr", 8.0},
         {"aec", 10.0}
     };
@@ -195,6 +196,25 @@ int main()
     //  List<scalar> table1vals(table1.begin(), table1.end());
     //  wordList table1keys(table1.begin(), table1.end());
 
+    Info<< "\nFrom table1: " << flatOutput(table1.sortedToc()) << nl
+        << "retain keys: " << flatOutput(table3.sortedToc()) << nl;
+
+    table1.retain(table3);
+    Info<< "-> " << flatOutput(table1.sortedToc()) << nl;
+
+    Info<< "Lookup non-existent" << nl;
+
+    Info<< table1.lookup("missing-const", 1.2345e+6)
+        << "  // const-access" << nl;
+
+    Info<< table1("missing-inadvertent", 3.14159)
+        << "  // (inadvertent?) non-const access"  << nl;
+
+    Info<< table1("missing-autovivify")
+        << "  // Known auto-vivification (non-const access)" << nl;
+
+    Info<<"\ntable1: " << table1 << endl;
+
     Info<< "\nDone\n";
 
     return 0;
diff --git a/src/OpenFOAM/containers/HashTables/HashSet/HashSet.C b/src/OpenFOAM/containers/HashTables/HashSet/HashSet.C
index 321b8dd5df..77ab200a42 100644
--- a/src/OpenFOAM/containers/HashTables/HashSet/HashSet.C
+++ b/src/OpenFOAM/containers/HashTables/HashSet/HashSet.C
@@ -227,16 +227,9 @@ void Foam::HashSet<Key, Hash>::operator|=(const HashSet<Key, Hash>& rhs)
 
 
 template<class Key, class Hash>
-void Foam::HashSet<Key, Hash>::operator&=(const HashSet<Key, Hash>& rhs)
+inline void Foam::HashSet<Key, Hash>::operator&=(const HashSet<Key, Hash>& rhs)
 {
-    // Remove elements not also found in rhs
-    for (iterator iter = this->begin(); iter != this->end(); ++iter)
-    {
-        if (!rhs.found(iter.key()))
-        {
-            this->erase(iter);
-        }
-    }
+    this->parent_type::retain(rhs);
 }
 
 
@@ -259,13 +252,9 @@ void Foam::HashSet<Key, Hash>::operator^=(const HashSet<Key, Hash>& rhs)
 
 
 template<class Key, class Hash>
-void Foam::HashSet<Key, Hash>::operator-=(const HashSet<Key, Hash>& rhs)
+inline void Foam::HashSet<Key, Hash>::operator-=(const HashSet<Key, Hash>& rhs)
 {
-    // Remove rhs elements from lhs
-    for (const_iterator iter = rhs.cbegin(); iter != rhs.cend(); ++iter)
-    {
-        this->erase(iter.key());
-    }
+    this->parent_type::erase(rhs);
 }
 
 
diff --git a/src/OpenFOAM/containers/HashTables/HashSet/HashSet.H b/src/OpenFOAM/containers/HashTables/HashSet/HashSet.H
index 300fc11132..d6171ad585 100644
--- a/src/OpenFOAM/containers/HashTables/HashSet/HashSet.H
+++ b/src/OpenFOAM/containers/HashTables/HashSet/HashSet.H
@@ -277,7 +277,7 @@ public:
         void operator|=(const HashSet<Key, Hash>& rhs);
 
         //- Only retain entries found in both HashSets
-        void operator&=(const HashSet<Key, Hash>& rhs);
+        inline void operator&=(const HashSet<Key, Hash>& rhs);
 
         //- Only retain unique entries (xor)
         void operator^=(const HashSet<Key, Hash>& rhs);
@@ -289,7 +289,7 @@ public:
         }
 
         //- Remove entries listed in the given HashSet from this HashSet
-        void operator-=(const HashSet<Key, Hash>& rhs);
+        inline void operator-=(const HashSet<Key, Hash>& rhs);
 
 
     // IOstream Operator
diff --git a/src/OpenFOAM/containers/HashTables/HashTable/HashTable.C b/src/OpenFOAM/containers/HashTables/HashTable/HashTable.C
index b0b96c5b19..5916a753bf 100644
--- a/src/OpenFOAM/containers/HashTables/HashTable/HashTable.C
+++ b/src/OpenFOAM/containers/HashTables/HashTable/HashTable.C
@@ -257,7 +257,7 @@ template<class T, class Key, class Hash>
 bool Foam::HashTable<T, Key, Hash>::set
 (
     const Key& key,
-    const T& newEntry,
+    const T& obj,
     const bool protect
 )
 {
@@ -284,7 +284,7 @@ bool Foam::HashTable<T, Key, Hash>::set
     if (!existing)
     {
         // Not found, insert it at the head
-        table_[hashIdx] = new hashedEntry(key, newEntry, table_[hashIdx]);
+        table_[hashIdx] = new hashedEntry(key, obj, table_[hashIdx]);
         nElmts_++;
 
         if (double(nElmts_)/tableSize_ > 0.8 && tableSize_ < maxTableSize)
@@ -316,7 +316,7 @@ bool Foam::HashTable<T, Key, Hash>::set
     {
         // Found - overwrite existing entry
         // this corresponds to the Perl convention
-        hashedEntry* ep = new hashedEntry(key, newEntry, existing->next_);
+        hashedEntry* ep = new hashedEntry(key, obj, existing->next_);
 
         // Replace existing element - within list or insert at the head
         if (prev)
@@ -450,15 +450,15 @@ Foam::label Foam::HashTable<T, Key, Hash>::erase
     const HashTable<AnyType, Key, AnyHash>& other
 )
 {
-    // Remove other keys from this table
     const label nTotal = this->size();
     label changed = 0;
 
-    if (other.size() < nTotal)
+    using other_iter =
+        typename HashTable<AnyType, Key, AnyHash>::const_iterator;
+
+    if (other.size() <= nTotal)
     {
-        // other is smaller, use its keys for removal
-        using other_iter =
-            typename HashTable<AnyType, Key, AnyHash>::const_iterator;
+        // The other is smaller/same-size, use its keys for removal
 
         for
         (
@@ -475,7 +475,7 @@ Foam::label Foam::HashTable<T, Key, Hash>::erase
     }
     else
     {
-        // other is same/larger: iterate ourselves and check for key in other
+        // We are smaller: remove if found in the other hash
         for
         (
             iterator iter = begin();
@@ -494,6 +494,39 @@ Foam::label Foam::HashTable<T, Key, Hash>::erase
 }
 
 
+template<class T, class Key, class Hash>
+template<class AnyType, class AnyHash>
+Foam::label Foam::HashTable<T, Key, Hash>::retain
+(
+    const HashTable<AnyType, Key, AnyHash>& other
+)
+{
+    const label nTotal = this->size();
+    label changed = 0;
+
+    if (other.empty())
+    {
+        // Trivial case
+        changed = nTotal;
+        this->clear();
+    }
+    else
+    {
+        // Inverted logic: remove if *not* found in the other hash
+
+        for (iterator iter = begin(); iter != end(); ++iter)
+        {
+            if (!other.found(iter.key()) && erase(iter))
+            {
+                ++changed;
+            }
+        }
+    }
+
+    return changed;
+}
+
+
 template<class T, class Key, class Hash>
 void Foam::HashTable<T, Key, Hash>::resize(const label sz)
 {
diff --git a/src/OpenFOAM/containers/HashTables/HashTable/HashTable.H b/src/OpenFOAM/containers/HashTables/HashTable/HashTable.H
index bd60050ee4..53cf8da553 100644
--- a/src/OpenFOAM/containers/HashTables/HashTable/HashTable.H
+++ b/src/OpenFOAM/containers/HashTables/HashTable/HashTable.H
@@ -44,6 +44,7 @@ Note
 SourceFiles
     HashTableI.H
     HashTable.C
+    HashTableCoreI.H
     HashTableCore.C
     HashTableIO.C
 
@@ -247,7 +248,7 @@ private:
 
         //- Assign a new hash-entry to a possibly already existing key.
         //  Return true if the new entry was set.
-        bool set(const Key& key, const T& newEntry, const bool protect);
+        bool set(const Key& key, const T& obj, const bool protect);
 
 
 protected:
@@ -307,17 +308,20 @@ public:
         //- Return true if the hash table is empty
         inline bool empty() const;
 
-        //- Return true if hashedEntry is found in table
+        //- Return true if hashed entry is found in table
         bool found(const Key& key) const;
 
-        //- Find and return an iterator set at the hashedEntry
+        //- Find and return an iterator set at the hashed entry
         //  If not found iterator = end()
         iterator find(const Key& key);
 
-        //- Find and return an const_iterator set at the hashedEntry
+        //- Find and return an const_iterator set at the hashed entry
         //  If not found iterator = end()
         const_iterator find(const Key& key) const;
 
+        //- Return hashed entry if it exists, or return the given default
+        inline const T& lookup(const Key& key, const T& deflt) const;
+
         //- Return the table of contents
         List<Key> toc() const;
 
@@ -327,42 +331,50 @@ public:
 
       // Edit
 
-        //- Insert a new hashedEntry
+        //- Insert a new entry
         //  Return true if the entry inserted, which means that it did
         //  not previously exist in the table.
-        inline bool insert(const Key& key, const T& newEntry);
+        inline bool insert(const Key& key, const T& obj);
 
-        //- Assign a new hashedEntry, overwriting existing entries.
+        //- Assign a new entry, overwriting existing entries.
         //  Returns true.
-        inline bool set(const Key& key, const T& newEntry);
+        inline bool set(const Key& key, const T& obj);
 
-        //- Erase a hashedEntry specified by given iterator
+        //- Erase an entry specified by given iterator
         //  This invalidates the iterator until the next ++ operation
         bool erase(const iterator& iter);
 
-        //- Erase a hashedEntry specified by the given key
+        //- Erase an entry specified by the given key
         bool erase(const Key& key);
 
-        //- Remove entries given by the listed keys from this HashTable
+        //- Remove table entries given by the listed keys
         //  Return the number of elements removed
         label erase(const UList<Key>& keys);
 
-        //- Remove entries given by the listed keys from this HashTable
+        //- Remove table entries given by the listed keys
         //  Return the number of elements removed
         template<unsigned Size>
         label erase(const FixedList<Key, Size>& keys);
 
-        //- Remove entries given by the listed keys from this HashTable
+        //- Remove table entries given by the listed keys
         //  Return the number of elements removed
         label erase(std::initializer_list<Key> keys);
 
-        //- Remove entries given by the given keys from this HashTable
+        //- Remove table entries given by keys of the other hash-table.
         //  Return the number of elements removed.
-        //  The parameter HashTable needs the same type of key, but the
+        //
+        //  The other hash-table must have the same type of key, but the
         //  type of values held and the hashing function are arbitrary.
         template<class AnyType, class AnyHash>
         label erase(const HashTable<AnyType, Key, AnyHash>& other);
 
+        //- Retain table entries given by keys of the other hash-table.
+        //
+        //  The other hash-table must have the same type of key, but the
+        //  type of values held and the hashing function are arbitrary.
+        template<class AnyType, class AnyHash>
+        label retain(const HashTable<AnyType, Key, AnyHash>& other);
+
         //- Resize the hash table for efficiency
         void resize(const label sz);
 
@@ -383,10 +395,10 @@ public:
 
     // Member Operators
 
-        //- Find and return a hashedEntry
+        //- Find and return a hashed entry. FatalError if it does not exist.
         inline T& operator[](const Key& key);
 
-        //- Find and return a hashedEntry
+        //- Find and return a hashed entry. FatalError if it does not exist.
         inline const T& operator[](const Key& key) const;
 
         //- Return existing entry or create a new entry.
@@ -394,6 +406,12 @@ public:
         //  value-initialized. For primitives, this will be zero.
         inline T& operator()(const Key& key);
 
+        //- Return existing entry or insert a new entry.
+        inline T& operator()(const Key& key, const T& deflt);
+
+        //- Return hashed entry if it exists, or return the given default
+        inline const T& operator()(const Key& key, const T& deflt) const;
+
         //- Assignment
         void operator=(const HashTable<T, Key, Hash>& rhs);
 
diff --git a/src/OpenFOAM/containers/HashTables/HashTable/HashTableI.H b/src/OpenFOAM/containers/HashTables/HashTable/HashTableI.H
index f8df243759..5391ca78b1 100644
--- a/src/OpenFOAM/containers/HashTables/HashTable/HashTableI.H
+++ b/src/OpenFOAM/containers/HashTables/HashTable/HashTableI.H
@@ -79,10 +79,10 @@ template<class T, class Key, class Hash>
 inline bool Foam::HashTable<T, Key, Hash>::insert
 (
     const Key& key,
-    const T& newEntry
+    const T& obj
 )
 {
-    return this->set(key, newEntry, true);
+    return this->set(key, obj, true);
 }
 
 
@@ -90,10 +90,10 @@ template<class T, class Key, class Hash>
 inline bool Foam::HashTable<T, Key, Hash>::set
 (
     const Key& key,
-    const T& newEntry
+    const T& obj
 )
 {
-    return this->set(key, newEntry, false);
+    return this->set(key, obj, false);
 }
 
 
@@ -105,6 +105,18 @@ Foam::HashTable<T, Key, Hash>::xfer()
 }
 
 
+template<class T, class Key, class Hash>
+inline const T& Foam::HashTable<T, Key, Hash>::lookup
+(
+    const Key& key,
+    const T& deflt
+) const
+{
+    const_iterator iter = this->find(key);
+    return iter.found() ? iter.object() : deflt;
+}
+
+
 // * * * * * * * * * * * * * * * Member Operators  * * * * * * * * * * * * * //
 
 template<class T, class Key, class Hash>
@@ -156,6 +168,36 @@ inline T& Foam::HashTable<T, Key, Hash>::operator()(const Key& key)
 }
 
 
+template<class T, class Key, class Hash>
+inline T& Foam::HashTable<T, Key, Hash>::operator()
+(
+    const Key& key,
+    const T& deflt
+)
+{
+    iterator iter = this->find(key);
+
+    if (iter.found())
+    {
+        return iter.object();
+    }
+
+    this->insert(key, deflt);
+    return find(key).object();
+}
+
+
+template<class T, class Key, class Hash>
+inline const T& Foam::HashTable<T, Key, Hash>::operator()
+(
+    const Key& key,
+    const T& deflt
+) const
+{
+    return this->lookup(key, deflt);
+}
+
+
 // * * * * * * * * * * * * * * * iterator base * * * * * * * * * * * * * * * //
 
 template<class T, class Key, class Hash>
diff --git a/src/OpenFOAM/containers/HashTables/StaticHashTable/StaticHashTable.C b/src/OpenFOAM/containers/HashTables/StaticHashTable/StaticHashTable.C
index 948a451d47..ec30dfc20a 100644
--- a/src/OpenFOAM/containers/HashTables/StaticHashTable/StaticHashTable.C
+++ b/src/OpenFOAM/containers/HashTables/StaticHashTable/StaticHashTable.C
@@ -203,7 +203,7 @@ template<class T, class Key, class Hash>
 bool Foam::StaticHashTable<T, Key, Hash>::set
 (
     const Key& key,
-    const T& newEntry,
+    const T& obj,
     const bool protect
 )
 {
@@ -229,7 +229,7 @@ bool Foam::StaticHashTable<T, Key, Hash>::set
         localObjects.setSize(existing+1);
 
         localKeys[existing] = key;
-        localObjects[existing] = newEntry;
+        localObjects[existing] = obj;
 
         nElmts_++;
     }
@@ -250,7 +250,7 @@ bool Foam::StaticHashTable<T, Key, Hash>::set
     {
         // Found - overwrite existing entry
         // this corresponds to the Perl convention
-        objects_[hashIdx][existing] = newEntry;
+        objects_[hashIdx][existing] = obj;
     }
 
     return true;
diff --git a/src/OpenFOAM/containers/HashTables/StaticHashTable/StaticHashTable.H b/src/OpenFOAM/containers/HashTables/StaticHashTable/StaticHashTable.H
index 639a434d65..5b0a3ef8a5 100644
--- a/src/OpenFOAM/containers/HashTables/StaticHashTable/StaticHashTable.H
+++ b/src/OpenFOAM/containers/HashTables/StaticHashTable/StaticHashTable.H
@@ -121,10 +121,10 @@ class StaticHashTable
 
         //- Return the hash index of the Key within the current table size.
         //  No checks for zero-sized tables.
-        inline label hashKeyIndex(const Key&) const;
+        inline label hashKeyIndex(const Key& key) const;
 
         //- Assign a new hashed entry to a possibly already existing key
-        bool set(const Key&, const T& newElmt, bool protect);
+        bool set(const Key& key, const T& obj, bool protect);
 
 
 public:
diff --git a/src/OpenFOAM/containers/HashTables/StaticHashTable/StaticHashTableI.H b/src/OpenFOAM/containers/HashTables/StaticHashTable/StaticHashTableI.H
index cebb3852aa..2e6b5db0ea 100644
--- a/src/OpenFOAM/containers/HashTables/StaticHashTable/StaticHashTableI.H
+++ b/src/OpenFOAM/containers/HashTables/StaticHashTable/StaticHashTableI.H
@@ -26,8 +26,6 @@ License
 #include "error.H"
 #include "IOstreams.H"
 
-// * * * * * * * * * * * * * Private Member Classes * * * * * * * * * * * * //
-
 // * * * * * * * * * * * * Private Member Functions  * * * * * * * * * * * * //
 
 template<class T, class Key, class Hash>
@@ -59,10 +57,10 @@ template<class T, class Key, class Hash>
 inline bool Foam::StaticHashTable<T, Key, Hash>::insert
 (
     const Key& key,
-    const T& newEntry
+    const T& obj
 )
 {
-    return set(key, newEntry, true);
+    return set(key, obj, true);
 }
 
 
@@ -70,10 +68,10 @@ template<class T, class Key, class Hash>
 inline bool Foam::StaticHashTable<T, Key, Hash>::set
 (
     const Key& key,
-    const T& newEntry
+    const T& obj
 )
 {
-    return set(key, newEntry, false);
+    return set(key, obj, false);
 }