diff --git a/.cproject b/.cproject
index 2f0f668ce..26815d331 100644
--- a/.cproject
+++ b/.cproject
@@ -1507,6 +1507,22 @@
 				<useDefaultCommand>true</useDefaultCommand>
 				<runAllBuilders>true</runAllBuilders>
 			</target>
+			<target name="tests/timeCalibratedCamera.run" path="build/gtsam/geometry" targetID="org.eclipse.cdt.build.MakeTargetBuilder">
+				<buildCommand>make</buildCommand>
+				<buildArguments>-j2</buildArguments>
+				<buildTarget>tests/timeCalibratedCamera.run</buildTarget>
+				<stopOnError>true</stopOnError>
+				<useDefaultCommand>true</useDefaultCommand>
+				<runAllBuilders>true</runAllBuilders>
+			</target>
+			<target name="tests/testPoint2.run" path="build/gtsam/geometry" targetID="org.eclipse.cdt.build.MakeTargetBuilder">
+				<buildCommand>make</buildCommand>
+				<buildArguments>-j2</buildArguments>
+				<buildTarget>tests/testPoint2.run</buildTarget>
+				<stopOnError>true</stopOnError>
+				<useDefaultCommand>true</useDefaultCommand>
+				<runAllBuilders>true</runAllBuilders>
+			</target>
 			<target name="all" path="slam" targetID="org.eclipse.cdt.build.MakeTargetBuilder">
 				<buildCommand>make</buildCommand>
 				<buildArguments>-j2</buildArguments>
diff --git a/gtsam/geometry/CalibratedCamera.cpp b/gtsam/geometry/CalibratedCamera.cpp
index a442e9357..fa27f2f71 100644
--- a/gtsam/geometry/CalibratedCamera.cpp
+++ b/gtsam/geometry/CalibratedCamera.cpp
@@ -61,22 +61,42 @@ Point2 CalibratedCamera::project(const Point3& point,
 		boost::optional<Matrix&> H1,
 		boost::optional<Matrix&> H2) const {
 
+#ifdef CALIBRATEDCAMERA_CHAIN_RULE
 	Point3 q = pose_.transform_to(point, H1, H2);
+#else
+	Point3 q = pose_.transform_to(point);
+#endif
+	Point2 intrinsic = project_to_camera(q);
 
 	// Check if point is in front of camera
 	if(q.z() <= 0)
 	  throw CheiralityException();
 
 	if (H1 || H2) {
-		Matrix H;
-		Point2 intrinsic = project_to_camera(q,H);
+#ifdef CALIBRATEDCAMERA_CHAIN_RULE
 		// just implement chain rule
+		Matrix H;
+		project_to_camera(q,H);
 		if (H1) *H1 = H * (*H1);
-		if (H1) *H2 = H * (*H2);
-		return intrinsic;
+		if (H2) *H2 = H * (*H2);
+#else
+		// optimized version, see CalibratedCamera.nb
+		const double z = q.z(), d = 1.0/z;
+		const double u = intrinsic.x(), v = intrinsic.y(), uv = u*v;
+		if (H1) *H1 = Matrix_(2,6,
+				      uv,-(1.+u*u), v, -d , 0., d*u,
+				(1.+v*v),      -uv,-u,  0.,-d , d*v
+		    );
+		if (H2) {
+			const Matrix R(pose_.rotation().matrix());
+			*H2 = d * Matrix_(2,3,
+					R(0,0) - u*R(0,2), R(1,0) - u*R(1,2), R(2,0) - u*R(2,2),
+					R(0,1) - v*R(0,2), R(1,1) - v*R(1,2), R(2,1) - v*R(2,2)
+		    );
+		}
+#endif
 	}
-	else
-		return project_to_camera(q);
+	return intrinsic;
 }
 
 /* ************************************************************************* */
diff --git a/gtsam/geometry/tests/testCalibratedCamera.cpp b/gtsam/geometry/tests/testCalibratedCamera.cpp
index 4be47a4c0..5bb1ebe65 100644
--- a/gtsam/geometry/tests/testCalibratedCamera.cpp
+++ b/gtsam/geometry/tests/testCalibratedCamera.cpp
@@ -78,10 +78,10 @@ TEST( CalibratedCamera, level2)
 /* ************************************************************************* */
 TEST( CalibratedCamera, project)
 {
-  CHECK(assert_equal( camera.project(point1), Point2(-.16,  .16) ));
-  CHECK(assert_equal( camera.project(point2), Point2(-.16, -.16) ));
-  CHECK(assert_equal( camera.project(point3), Point2( .16, -.16) ));
-  CHECK(assert_equal( camera.project(point4), Point2( .16,  .16) ));
+  CHECK(assert_equal( Point2(-.16,  .16), camera.project(point1) ));
+	CHECK(assert_equal( Point2(-.16, -.16), camera.project(point2) ));
+	CHECK(assert_equal( Point2( .16, -.16), camera.project(point3) ));
+	CHECK(assert_equal( Point2( .16,  .16), camera.project(point4) ));
 }
 
 /* ************************************************************************* */
@@ -105,9 +105,10 @@ TEST( CalibratedCamera, Dproject_point_pose)
 	Point2 result = camera.project(point1, Dpose, Dpoint);
 	Matrix numerical_pose  = numericalDerivative21(project2, pose1, point1);
 	Matrix numerical_point = numericalDerivative22(project2, pose1, point1);
-	CHECK(assert_equal(result, Point2(-.16,  .16) ));
-	CHECK(assert_equal(Dpose,  numerical_pose, 1e-7));
-	CHECK(assert_equal(Dpoint, numerical_point,1e-7));
+	CHECK(assert_equal(Point3(-0.08, 0.08, 0.5), camera.pose().transform_to(point1)));
+	CHECK(assert_equal(Point2(-.16,  .16), result));
+	CHECK(assert_equal(numerical_pose,  Dpose, 1e-7));
+	CHECK(assert_equal(numerical_point, Dpoint, 1e-7));
 }
 
 /* ************************************************************************* */