diff --git a/gtsam/geometry/OrientedPlane3.cpp b/gtsam/geometry/OrientedPlane3.cpp
index 82207d4ce..5cfa80779 100644
--- a/gtsam/geometry/OrientedPlane3.cpp
+++ b/gtsam/geometry/OrientedPlane3.cpp
@@ -83,11 +83,12 @@ Vector3 OrientedPlane3::errorVector(const OrientedPlane3& other, OptionalJacobia
 }
 
 /* ************************************************************************* */
-OrientedPlane3 OrientedPlane3::retract(const Vector3& v, OptionalJacobian<4,3> H) const {
-  Matrix32 H_n;
+OrientedPlane3 OrientedPlane3::retract(const Vector3& v,
+                                       OptionalJacobian<3,3> H) const {
+  Matrix22 H_n;
   Unit3 n_retract (n_.retract(Vector2(v(0), v(1)), H? &H_n : nullptr));
   if (H) {
-    *H << H_n, Vector3::Zero(), 0, 0, 1;
+    *H << H_n, Vector2::Zero(), 0, 0, 1;
   }
   return OrientedPlane3(n_retract, d_ + v(2));
 }
diff --git a/gtsam/geometry/OrientedPlane3.h b/gtsam/geometry/OrientedPlane3.h
index 7306942f2..596118385 100644
--- a/gtsam/geometry/OrientedPlane3.h
+++ b/gtsam/geometry/OrientedPlane3.h
@@ -134,7 +134,7 @@ public:
   }
 
   /// The retract function
-  OrientedPlane3 retract(const Vector3& v, OptionalJacobian<4,3> H = boost::none) const;
+  OrientedPlane3 retract(const Vector3& v, OptionalJacobian<3,3> H = boost::none) const;
 
   /// The local coordinates function
   Vector3 localCoordinates(const OrientedPlane3& s) const;
diff --git a/gtsam/geometry/tests/testOrientedPlane3.cpp b/gtsam/geometry/tests/testOrientedPlane3.cpp
index 1ad2b0405..54cf84ea8 100644
--- a/gtsam/geometry/tests/testOrientedPlane3.cpp
+++ b/gtsam/geometry/tests/testOrientedPlane3.cpp
@@ -161,39 +161,23 @@ TEST (OrientedPlane3, error2) {
   EXPECT(assert_equal(expectedH2, actualH2, 1e-9));
 }
 
-//*******************************************************************************
-// Wrapper to make retract return a Vector3 so we can test numerical derivatives.
-Vector4 RetractTest(const OrientedPlane3& plane, const Vector3& v,
-                    OptionalJacobian<4, 3> H) {
-  OrientedPlane3 plane_retract = plane.retract(v, H);
-  return Vector4(plane_retract.normal().point3().x(),
-                 plane_retract.normal().point3().y(),
-                 plane_retract.normal().point3().z(),
-                 plane_retract.distance());
-}
-
 //*******************************************************************************
 TEST (OrientedPlane3, jacobian_retract) {
   OrientedPlane3 plane(-1, 0.1, 0.2, 5);
-  Matrix43 H;
+  Matrix33 H_actual;
+  boost::function<OrientedPlane3(const Vector3&)> f =
+      boost::bind(&OrientedPlane3::retract, plane, _1, boost::none);
   {
       Vector3 v (-0.1, 0.2, 0.3);
-      plane.retract(v, H);
-      // Test that jacobian is numerically as expected.
-      boost::function<Vector4(const OrientedPlane3&, const Vector3&)> f =
-          boost::bind(RetractTest, _1, _2, boost::none);
-      Matrix43 H_expected_numerical = numericalDerivative22(f, plane, v);
-      EXPECT(assert_equal(H_expected_numerical, H, 1e-9));
+      plane.retract(v, H_actual);
+      Matrix H_expected_numerical = numericalDerivative11(f, v);
+      EXPECT(assert_equal(H_expected_numerical, H_actual, 1e-9));
   }
   {
-      Matrix43 H;
       Vector3 v (0, 0, 0);
-      plane.retract(v, H);
-      // Test that jacobian is numerically as expected.
-      boost::function<Vector4(const OrientedPlane3&, const Vector3&)> f =
-          boost::bind(RetractTest, _1, _2, boost::none);
-      Matrix43 H_expected_numerical = numericalDerivative22(f, plane, v);
-      EXPECT(assert_equal(H_expected_numerical, H, 1e-9));
+      plane.retract(v, H_actual);
+      Matrix H_expected_numerical = numericalDerivative11(f, v);
+      EXPECT(assert_equal(H_expected_numerical, H_actual, 1e-9));
   }
 }