diff --git a/gtsam/inference/EliminationTree-inst.h b/gtsam/inference/EliminationTree-inst.h
index 33ba6e18d..3390a3aac 100644
--- a/gtsam/inference/EliminationTree-inst.h
+++ b/gtsam/inference/EliminationTree-inst.h
@@ -98,7 +98,7 @@ namespace gtsam {
       for (size_t j = 0; j < n; j++)
       {
         // Retrieve the factors involving this variable and create the current node
-        const VariableIndex::Factors& factors = structure[order[j]];
+        const FactorIndices& factors = structure[order[j]];
         const sharedNode node = boost::make_shared<Node>();
         node->key = order[j];
 
diff --git a/gtsam/inference/Ordering.cpp b/gtsam/inference/Ordering.cpp
index 1165b4a0f..da61ca57e 100644
--- a/gtsam/inference/Ordering.cpp
+++ b/gtsam/inference/Ordering.cpp
@@ -79,7 +79,7 @@ Ordering Ordering::ColamdConstrained(const VariableIndex& variableIndex,
   size_t index = 0;
   for (auto key_factors: variableIndex) {
     // Arrange factor indices into COLAMD format
-    const VariableIndex::Factors& column = key_factors.second;
+    const FactorIndices& column = key_factors.second;
     for(size_t factorIndex: column) {
       A[count++] = (int) factorIndex; // copy sparse column
     }
diff --git a/gtsam/inference/VariableIndex-inl.h b/gtsam/inference/VariableIndex-inl.h
index bc8100e4a..727ef8fd8 100644
--- a/gtsam/inference/VariableIndex-inl.h
+++ b/gtsam/inference/VariableIndex-inl.h
@@ -67,8 +67,8 @@ void VariableIndex::remove(ITERATOR firstFactor, ITERATOR lastFactor,
           "Internal error, requested inconsistent number of factor indices and factors in VariableIndex::remove");
     if (factors[i]) {
       for(Key j: *factors[i]) {
-        Factors& factorEntries = internalAt(j);
-        Factors::iterator entry = std::find(factorEntries.begin(),
+        FactorIndices& factorEntries = internalAt(j);
+        auto entry = std::find(factorEntries.begin(),
             factorEntries.end(), *factorIndex);
         if (entry == factorEntries.end())
           throw std::invalid_argument(
diff --git a/gtsam/inference/VariableIndex.h b/gtsam/inference/VariableIndex.h
index a96a53289..0d7320428 100644
--- a/gtsam/inference/VariableIndex.h
+++ b/gtsam/inference/VariableIndex.h
@@ -41,26 +41,22 @@ namespace gtsam {
  * \nosubgrouping
  */
 class GTSAM_EXPORT VariableIndex {
-public:
-
+ public:
   typedef boost::shared_ptr<VariableIndex> shared_ptr;
-  typedef FactorIndices Factors;
-  typedef Factors::iterator Factor_iterator;
-  typedef Factors::const_iterator Factor_const_iterator;
+  typedef FactorIndices::iterator Factor_iterator;
+  typedef FactorIndices::const_iterator Factor_const_iterator;
 
-protected:
-  typedef FastMap<Key,Factors> KeyMap;
+ protected:
+  typedef FastMap<Key, FactorIndices> KeyMap;
   KeyMap index_;
-  size_t nFactors_; // Number of factors in the original factor graph.
-  size_t nEntries_; // Sum of involved variable counts of each factor.
+  size_t nFactors_;  // Number of factors in the original factor graph.
+  size_t nEntries_;  // Sum of involved variable counts of each factor.
 
-public:
+ public:
   typedef KeyMap::const_iterator const_iterator;
   typedef KeyMap::const_iterator iterator;
   typedef KeyMap::value_type value_type;
 
-public:
-
   /// @name Standard Constructors
   /// @{
 
@@ -71,8 +67,10 @@ public:
    * Create a VariableIndex that computes and stores the block column structure
    * of a factor graph.
    */
-  template<class FG>
-  VariableIndex(const FG& factorGraph) : nFactors_(0), nEntries_(0) { augment(factorGraph); }
+  template <class FG>
+  explicit VariableIndex(const FG& factorGraph) : nFactors_(0), nEntries_(0) {
+    augment(factorGraph);
+  }
 
   /// @}
   /// @name Standard Interface
@@ -88,7 +86,7 @@ public:
   size_t nEntries() const { return nEntries_; }
 
   /// Access a list of factors by variable
-  const Factors& operator[](Key variable) const {
+  const FactorIndices& operator[](Key variable) const {
     KeyMap::const_iterator item = index_.find(variable);
     if(item == index_.end())
       throw std::invalid_argument("Requested non-existent variable from VariableIndex");
@@ -96,6 +94,11 @@ public:
     return item->second;
   }
 
+  /// Return true if no factors associated with a variable
+  const bool empty(Key variable) const {
+    return (*this)[variable].empty();
+  }
+
   /// @}
   /// @name Testable
   /// @{
@@ -166,16 +169,18 @@ protected:
   Factor_const_iterator factorsEnd(Key variable) const { return internalAt(variable).end(); }
 
   /// Internal version of 'at' that asserts existence
-  const Factors& internalAt(Key variable) const {
+  const FactorIndices& internalAt(Key variable) const {
     const KeyMap::const_iterator item = index_.find(variable);
     assert(item != index_.end());
-    return item->second; }
+    return item->second; 
+  }
 
   /// Internal version of 'at' that asserts existence
-  Factors& internalAt(Key variable) {
+  FactorIndices& internalAt(Key variable) {
     const KeyMap::iterator item = index_.find(variable);
     assert(item != index_.end());
-    return item->second; }
+    return item->second; 
+  }
 
   /// @}
 };
diff --git a/gtsam_unstable/discrete/CSP.cpp b/gtsam_unstable/discrete/CSP.cpp
index cf5abdcb1..0223250b5 100644
--- a/gtsam_unstable/discrete/CSP.cpp
+++ b/gtsam_unstable/discrete/CSP.cpp
@@ -43,7 +43,7 @@ namespace gtsam {
         // keep track of which domains changed
         changed[v] = false;
         // loop over all factors/constraints for variable v
-        const VariableIndex::Factors& factors = index[v];
+        const FactorIndices& factors = index[v];
         for(size_t f: factors) {
           // if not already a singleton
           if (!domains[v].isSingleton()) {