diff --git a/gtsam/base/Group.h b/gtsam/base/Group.h
index aec4b5f1c..f97be5376 100644
--- a/gtsam/base/Group.h
+++ b/gtsam/base/Group.h
@@ -13,8 +13,9 @@
  * @file Group.h
  *
  * @brief Concept check class for variable types with Group properties
- * @date Nov 5, 2011
+ * @date November, 2011
  * @author Alex Cunningham
+ * @author Frank Dellaert
  */
 
 #pragma once
@@ -83,21 +84,34 @@ check_group_invariants(const G& a, const G& b, double tol = 1e-9) {
       && traits<G>::Equals(traits<G>::Compose(a, traits<G>::Between(a, b)), b, tol);
 }
 
-/// Macro to add group traits, additive flavor
-#define GTSAM_ADDITIVE_GROUP(GROUP) \
-    typedef additive_group_tag group_flavor; \
-    static GROUP Compose(const GROUP &g, const GROUP & h) { return g + h;} \
-    static GROUP Between(const GROUP &g, const GROUP & h) { return h - g;} \
-    static GROUP Inverse(const GROUP &g) { return -g;}
+namespace internal {
 
-/// Macro to add group traits, multiplicative flavor
-#define GTSAM_MULTIPLICATIVE_GROUP(GROUP) \
-    typedef additive_group_tag group_flavor; \
-    static GROUP Compose(const GROUP &g, const GROUP & h) { return g * h;} \
-    static GROUP Between(const GROUP &g, const GROUP & h) { return g.inverse() * h;} \
-    static GROUP Inverse(const GROUP &g) { return g.inverse();}
+/// A helper class that implements the traits interface for groups.
+template<class Class>
+struct GroupTraits {
+  typedef group_tag structure_category;
+  static Class Identity() { return Class::Identity(); }
+};
 
-} // \ namespace gtsam
+/// A helper class that implements the traits interface for additive groups.
+template<class Class>
+struct AdditiveGroupTraits : GroupTraits<Class> {
+    typedef additive_group_tag group_flavor; \
+    static Class Compose(const Class &g, const Class & h) { return g + h;} \
+    static Class Between(const Class &g, const Class & h) { return h - g;} \
+    static Class Inverse(const Class &g) { return -g;}
+};
+
+/// A helper class that implements the traits interface for multiplicative groups.
+template<class Class>
+struct MultiplicativeGroupTraits : GroupTraits<Class> {
+    typedef additive_group_tag group_flavor; \
+    static Class Compose(const Class &g, const Class & h) { return g * h;} \
+    static Class Between(const Class &g, const Class & h) { return g.inverse() * h;} \
+    static Class Inverse(const Class &g) { return g.inverse();}
+};
+}  // namespace internal
+}  // namespace gtsam
 
 /**
  * Macros for using the IsGroup
diff --git a/gtsam/geometry/Cyclic.h b/gtsam/geometry/Cyclic.h
index 2c883707f..8aa205aa3 100644
--- a/gtsam/geometry/Cyclic.h
+++ b/gtsam/geometry/Cyclic.h
@@ -16,10 +16,8 @@
  **/
 
 #include <gtsam/base/Group.h>
-#include <cstddef>
-#include <string>
-#include <iostream>
-#include <assert.h>
+#include <gtsam/base/Testable.h>
+#include <iostream> // for cout :-(
 
 namespace gtsam {
 
@@ -33,7 +31,7 @@ public:
       i_(i) {
     assert(i < N);
   }
-  /// Idenity element
+  /// Identity element
   static Cyclic Identity() {
     return Cyclic(0);
   }
@@ -63,20 +61,10 @@ public:
   }
 };
 
-/// Define cyclic group traits to be a model of the Group concept
+/// Define cyclic group traits to be a model of the Additive Group concept
 template<size_t N>
-struct traits<Cyclic<N> > {
-  typedef group_tag structure_category;GTSAM_ADDITIVE_GROUP(Cyclic<N>)
-  static Cyclic<N> Identity() {
-    return Cyclic<N>::Identity();
-  }
-  static bool Equals(const Cyclic<N>& a, const Cyclic<N>& b,
-      double tol = 1e-9) {
-    return a.equals(b, tol);
-  }
-  static void Print(const Cyclic<N>& c, const std::string &s = "") {
-    c.print(s);
-  }
+struct traits<Cyclic<N> > : internal::AdditiveGroupTraits<Cyclic<N> >, //
+    Testable<Cyclic<N> > {
 };
 
 } // \namespace gtsam