diff --git a/gtsam/geometry/tests/testRot3Q.cpp b/gtsam/geometry/tests/testRot3Q.cpp
index 65ca9e067..d7d43b33f 100644
--- a/gtsam/geometry/tests/testRot3Q.cpp
+++ b/gtsam/geometry/tests/testRot3Q.cpp
@@ -15,20 +15,65 @@
  * @author  Alireza Fathi
  */
 
-#include <gtsam/geometry/Point3.h>
 #include <gtsam/geometry/Rot3.h>
+#include <gtsam/geometry/Quaternion.h>
 
 #include <gtsam/base/Testable.h>
 #include <gtsam/base/numericalDerivative.h>
-#include <gtsam/base/lieProxies.h>
-
-#include <boost/math/constants/constants.hpp>
 
 #include <CppUnitLite/TestHarness.h>
 
+using namespace std;
+using namespace gtsam;
+
 #ifdef GTSAM_USE_QUATERNIONS
 
-// No quaternion only tests
+//******************************************************************************
+TEST(Rot3Q , Compare) {
+  using boost::none;
+
+  // We set up expected values with quaternions
+  typedef Quaternion Q;
+  typedef traits<Q> TQ;
+  typedef TQ::ChartJacobian OJ;
+
+  // We check Rot3 expressions
+  typedef Rot3 R;
+  typedef traits<R> TR;
+
+  // Define test values
+  Q q1(Eigen::AngleAxisd(1, Vector3(0, 0, 1)));
+  Q q2(Eigen::AngleAxisd(2, Vector3(0, 1, 0)));
+  R R1(q1), R2(q2);
+
+  // Check Compose
+  Q q3 = TQ::Compose(q1, q2, none, none);
+  R R3 = TR::Compose(R1, R2, none, none);
+  EXPECT(assert_equal(R(q3), R3));
+
+  // Check Retract/Local
+  Vector3 v(1e-5, 0, 0);
+  Vector3 vQ = TQ::Local(q3, TQ::Retract(q3, v));
+  Vector3 vR = TR::Local(R3, TR::Retract(R3, v));
+  EXPECT(assert_equal(vQ, vR));
+
+  // Check Retract/Local of Compose
+  Vector3 vQ1 = TQ::Local(q3, TQ::Compose(q1, TQ::Retract(q2, v)));
+  Vector3 vR1 = TR::Local(R3, TR::Compose(R1, TR::Retract(R2, v)));
+  EXPECT(assert_equal(vQ1, vR1));
+  Vector3 vQ2 = TQ::Local(q3, TQ::Compose(q1, TQ::Retract(q2, -v)));
+  Vector3 vR2 = TR::Local(R3, TR::Compose(R1, TR::Retract(R2, -v)));
+  EXPECT(assert_equal(vQ2, vR2));
+  EXPECT(assert_equal<Vector3>((vQ1 - vQ2) / 0.2, (vR1 - vR2) / 0.2));
+  cout << (vR1 - vR2) / 0.2 << endl;
+
+  // Check Compose Derivatives
+  Matrix HQ, HR;
+  HQ = numericalDerivative42<Q, Q, Q, OJ, OJ>(TQ::Compose, q1, q2, none, none);
+  HR = numericalDerivative42<R, R, R, OJ, OJ>(TR::Compose, R1, R2, none, none);
+  EXPECT(assert_equal(HQ, HR));
+
+}
 
 #endif