diff --git a/gtsam/geometry/Rot2.h b/gtsam/geometry/Rot2.h
index 23af69529..8ec39a6ba 100644
--- a/gtsam/geometry/Rot2.h
+++ b/gtsam/geometry/Rot2.h
@@ -106,7 +106,13 @@ namespace gtsam {
     inline size_t dim() const { return dimension; }
 
     /** Compose - make a new rotation by adding angles */
-    inline Rot2 compose(const Rot2& R1) const { return *this * R1;}
+    inline Rot2 compose(const Rot2& R1,
+        boost::optional<Matrix&> H1=boost::none,
+        boost::optional<Matrix&> H2=boost::none) const {
+      if(H1) *H1 = eye(1);
+      if(H2) *H2 = eye(1);
+      return *this * R1;
+    }
 
     /** Expmap around identity - create a rotation from an angle */
     static Rot2 Expmap(const Vector& v) {
@@ -126,7 +132,13 @@ namespace gtsam {
     inline Vector logmap(const Rot2& p2) const { return Logmap(between(p2));}
 
     /** Between using the default implementation */
-    inline Rot2 between(const Rot2& p2) const { return between_default(*this, p2); }
+    inline Rot2 between(const Rot2& p2,
+        boost::optional<Matrix&> H1=boost::none,
+        boost::optional<Matrix&> H2=boost::none) const {
+      if(H1) *H1 = -eye(1);
+      if(H2) *H2 = eye(1);
+      return between_default(*this, p2);
+    }
 
     /** return 2*2 rotation matrix */
     Matrix matrix() const;
diff --git a/gtsam/geometry/tests/testRot2.cpp b/gtsam/geometry/tests/testRot2.cpp
index 6df2939d1..6ecccac2c 100644
--- a/gtsam/geometry/tests/testRot2.cpp
+++ b/gtsam/geometry/tests/testRot2.cpp
@@ -44,6 +44,23 @@ TEST( Rot2, compose)
 {
 	CHECK(assert_equal(Rot2::fromAngle(0.45), Rot2::fromAngle(0.2)*Rot2::fromAngle(0.25)));
 	CHECK(assert_equal(Rot2::fromAngle(0.45), Rot2::fromAngle(0.25)*Rot2::fromAngle(0.2)));
+
+	Matrix H1, H2;
+	(void) Rot2::fromAngle(1.0).compose(Rot2::fromAngle(2.0), H1, H2);
+	EXPECT(assert_equal(eye(1), H1));
+  EXPECT(assert_equal(eye(1), H2));
+}
+
+/* ************************************************************************* */
+TEST( Rot2, between)
+{
+  CHECK(assert_equal(Rot2::fromAngle(0.05), Rot2::fromAngle(0.2).between(Rot2::fromAngle(0.25))));
+  CHECK(assert_equal(Rot2::fromAngle(-0.05), Rot2::fromAngle(0.25).between(Rot2::fromAngle(0.2))));
+
+  Matrix H1, H2;
+  (void) Rot2::fromAngle(1.0).between(Rot2::fromAngle(2.0), H1, H2);
+  EXPECT(assert_equal(-eye(1), H1));
+  EXPECT(assert_equal(eye(1), H2));
 }
 
 /* ************************************************************************* */