diff --git a/gtsam/nonlinear/NonlinearConjugateGradientOptimizer.cpp b/gtsam/nonlinear/NonlinearConjugateGradientOptimizer.cpp
index 403c72908..211acc78d 100644
--- a/gtsam/nonlinear/NonlinearConjugateGradientOptimizer.cpp
+++ b/gtsam/nonlinear/NonlinearConjugateGradientOptimizer.cpp
@@ -49,19 +49,23 @@ NonlinearConjugateGradientOptimizer::NonlinearConjugateGradientOptimizer(
       params_(params) {}
 
 double NonlinearConjugateGradientOptimizer::System::error(
-    const Values& state) const {
+    const State& state) const {
   return graph_.error(state);
 }
 
-VectorValues NonlinearConjugateGradientOptimizer::System::gradient(
-    const Values& state) const {
+NonlinearConjugateGradientOptimizer::System::Gradient
+NonlinearConjugateGradientOptimizer::System::gradient(
+    const State& state) const {
   return gradientInPlace(graph_, state);
 }
 
-Values NonlinearConjugateGradientOptimizer::System::advance(
-    const Values& current, const double alpha,
-    const VectorValues& gradient) const {
-  return current.retract(alpha * gradient);
+NonlinearConjugateGradientOptimizer::System::State
+NonlinearConjugateGradientOptimizer::System::advance(const State& current,
+                                                     const double alpha,
+                                                     const Gradient& g) const {
+  Gradient step = g;
+  step *= alpha;
+  return current.retract(step);
 }
 
 GaussianFactorGraph::shared_ptr NonlinearConjugateGradientOptimizer::iterate() {
diff --git a/gtsam/nonlinear/NonlinearConjugateGradientOptimizer.h b/gtsam/nonlinear/NonlinearConjugateGradientOptimizer.h
index 26f596b06..f662403dc 100644
--- a/gtsam/nonlinear/NonlinearConjugateGradientOptimizer.h
+++ b/gtsam/nonlinear/NonlinearConjugateGradientOptimizer.h
@@ -29,6 +29,8 @@ class GTSAM_EXPORT NonlinearConjugateGradientOptimizer : public NonlinearOptimiz
   /* a class for the nonlinearConjugateGradient template */
   class System {
   public:
+    typedef Values State;
+    typedef VectorValues Gradient;
     typedef NonlinearOptimizerParams Parameters;
 
   protected:
@@ -38,10 +40,10 @@ class GTSAM_EXPORT NonlinearConjugateGradientOptimizer : public NonlinearOptimiz
     System(const NonlinearFactorGraph &graph) :
         graph_(graph) {
     }
-    double error(const Values &state) const;
-    VectorValues gradient(const Values &state) const;
-    Values advance(const Values &current, const double alpha,
-                  const VectorValues &g) const;
+    double error(const State &state) const;
+    Gradient gradient(const State &state) const;
+    State advance(const State &current, const double alpha,
+                  const Gradient &g) const;
   };
 
 public:
@@ -162,8 +164,8 @@ std::tuple<V, int> nonlinearConjugateGradient(const S &system,
   }
 
   V currentValues = initial;
-  VectorValues currentGradient = system.gradient(currentValues), prevGradient,
-               direction = currentGradient;
+  typename S::Gradient currentGradient = system.gradient(currentValues),
+                       prevGradient, direction = currentGradient;
 
   /* do one step of gradient descent */
   V prevValues = currentValues;