diff --git a/gtsam/navigation/tests/testPreintegratedRotation.cpp b/gtsam/navigation/tests/testPreintegratedRotation.cpp
index bcd291eb2..d84af031e 100644
--- a/gtsam/navigation/tests/testPreintegratedRotation.cpp
+++ b/gtsam/navigation/tests/testPreintegratedRotation.cpp
@@ -74,11 +74,18 @@ TEST(PreintegratedRotation, integrateGyroMeasurement) {
   EQUALITY(Vector3(-deltaT * delta, 0, 0), expected.logmap(corrected))
   EXPECT(assert_equal(Rot3::Roll((omega - delta) * deltaT), corrected, 1e-9))
 
-  // TODO(frank): again the derivative is not the *sane* one!
-  // auto g = [&](const Vector3& increment) {
-  //   return pim.biascorrectedDeltaRij(increment, {});
-  // };
-  // EXPECT(assert_equal(numericalDerivative11<Rot3, Vector3>(g, Z_3x1), H));
+  auto g = [&](const Vector3& increment) {
+    return pim.biascorrectedDeltaRij(increment, {});
+  };
+  const Matrix3 sane = numericalDerivative11<Rot3, Vector3>(g, Z_3x1);
+  EXPECT(assert_equal(sane, pim.delRdelBiasOmega()));
+  // TODO(frank): the derivative H we compute in biascorrectedDeltaRij is not the *sane* one!
+  // EXPECT(assert_equal(sane, H));
+
+  // Let's integrate a second IMU measurement and check the Jacobian update:
+  pim.integrateGyroMeasurement(measuredOmega, bias, deltaT);
+  const Matrix3 sane2 = numericalDerivative11<Rot3, Vector3>(g, Z_3x1);
+  EXPECT(assert_equal(sane2, pim.delRdelBiasOmega()));
 }
 
 //******************************************************************************
@@ -124,11 +131,68 @@ TEST(PreintegratedRotation, integrateGyroMeasurementWithTransform) {
   EQUALITY(Vector3(0, -deltaT * delta, 0), expected.logmap(corrected))
   EXPECT(assert_equal(Rot3::Pitch((omega - delta) * deltaT), corrected, 1e-9))
 
-  // TODO(frank): again the derivative is not the *sane* one!
-  // auto g = [&](const Vector3& increment) {
-  //   return pim.biascorrectedDeltaRij(increment, {});
-  // };
-  // EXPECT(assert_equal(numericalDerivative11<Rot3, Vector3>(g, Z_3x1), H));
+  auto g = [&](const Vector3& increment) {
+    return pim.biascorrectedDeltaRij(increment, {});
+  };
+  const Matrix3 sane = numericalDerivative11<Rot3, Vector3>(g, Z_3x1);
+  EXPECT(assert_equal(sane, pim.delRdelBiasOmega()));
+  // TODO(frank): the derivative H we compute in biascorrectedDeltaRij is not the *sane* one!
+  // EXPECT(assert_equal(sane, H));
+
+  // Let's integrate a second IMU measurement and check the Jacobian update:
+  pim.integrateGyroMeasurement(measuredOmega, bias, deltaT);
+  const Matrix3 sane2 = numericalDerivative11<Rot3, Vector3>(g, Z_3x1);
+  EXPECT(assert_equal(sane2, pim.delRdelBiasOmega()));
+}
+
+// Create params we have a non-axis-aligned rotation and even an offset.
+static std::shared_ptr<PreintegratedRotationParams> paramsWithArbitraryTransform() {
+  auto p = std::make_shared<PreintegratedRotationParams>();
+  p->setBodyPSensor({Rot3::Expmap({1,2,3}), {4,5,6}});
+  return p;
+}
+
+TEST(PreintegratedRotation, integrateGyroMeasurementWithArbitraryTransform) {
+  // Example with a non-axis-aligned transform and some position.
+  using namespace biased_x_rotation;
+  auto p = paramsWithArbitraryTransform();
+
+  // Check the derivative:
+  Matrix3 H_bias;
+  const internal::IncrementalRotation f{measuredOmega, deltaT, p->getBodyPSensor()};
+  f(bias, H_bias);
+  EXPECT(assert_equal(numericalDerivative11<Rot3, Vector3>(f, bias), H_bias))
+
+  // Check derivative of deltaRij() after integration.
+  Matrix3 F;
+  PreintegratedRotation pim(p);
+  pim.integrateGyroMeasurement(measuredOmega, bias, deltaT, F);
+
+  // Check that system matrix F is the first derivative of compose:
+  EXPECT(assert_equal<Matrix3>(pim.deltaRij().inverse().AdjointMap(), F))
+
+  // Make sure delRdelBiasOmega is H_bias after integration.
+  EXPECT(assert_equal<Matrix3>(H_bias, pim.delRdelBiasOmega()))
+
+  // Check the bias correction in same way, but will now yield pitch change.
+  Matrix3 H;
+  const double delta = 0.05;
+  const Vector3 biasOmegaIncr(delta, 0, 0);
+  Rot3 corrected = pim.biascorrectedDeltaRij(biasOmegaIncr, H);
+
+  auto g = [&](const Vector3& increment) {
+    return pim.biascorrectedDeltaRij(increment, {});
+  };
+  const Matrix3 sane = numericalDerivative11<Rot3, Vector3>(g, Z_3x1);
+  EXPECT(assert_equal(sane, pim.delRdelBiasOmega()));
+  // TODO(frank): the derivative H we compute in biascorrectedDeltaRij is not the *sane* one!
+  // EXPECT(assert_equal(sane, H));
+
+  // Let's integrate a second IMU measurement and check the Jacobian update:
+  pim.integrateGyroMeasurement(measuredOmega, bias, deltaT);
+  const Matrix3 sane2 = numericalDerivative11<Rot3, Vector3>(g, Z_3x1);
+  EXPECT(assert_equal(sane2, pim.delRdelBiasOmega()));
+
 }
 
 //******************************************************************************