diff --git a/gtsam/geometry/Pose3.cpp b/gtsam/geometry/Pose3.cpp
index 0a56e2ef5..e505e8dff 100644
--- a/gtsam/geometry/Pose3.cpp
+++ b/gtsam/geometry/Pose3.cpp
@@ -198,7 +198,7 @@ Vector6 Pose3::ChartAtOrigin::Local(const Pose3& pose, ChartJacobian Hpose) {
  *  (see Chirikjian11book2, pg 44, eq 10.95.
  *  The closed-form formula is similar to formula 102 in Barfoot14tro)
  */
-static Matrix3 computeQforExpmapDerivative(const Vector6& xi) {
+Matrix3 Pose3::computeQforExpmapDerivative(const Vector6& xi, double nearZeroThreshold) {
   const auto w = xi.head<3>();
   const auto v = xi.tail<3>();
   const Matrix3 V = skewSymmetric(v);
@@ -220,7 +220,7 @@ static Matrix3 computeQforExpmapDerivative(const Vector6& xi) {
 #else
   // The closed-form formula in Barfoot14tro eq. (102)
   double phi = w.norm();
-  if (std::abs(phi)>1e-5) {
+  if (std::abs(phi)>nearZeroThreshold) {
     const double sinPhi = sin(phi), cosPhi = cos(phi);
     const double phi2 = phi * phi, phi3 = phi2 * phi, phi4 = phi3 * phi, phi5 = phi4 * phi;
     // Invert the sign of odd-order terms to have the right Jacobian
diff --git a/gtsam/geometry/Pose3.h b/gtsam/geometry/Pose3.h
index 159fd2927..575fbaa5c 100644
--- a/gtsam/geometry/Pose3.h
+++ b/gtsam/geometry/Pose3.h
@@ -181,6 +181,9 @@ public:
     static Vector6 Local(const Pose3& pose, ChartJacobian Hpose = boost::none);
   };
 
+  static Matrix3 computeQforExpmapDerivative(
+      const Vector6& xi, double nearZeroThreshold = 1e-5);
+
   using LieGroup<Pose3, 6>::inverse; // version with derivative
 
   /**
diff --git a/gtsam/geometry/tests/testPose3.cpp b/gtsam/geometry/tests/testPose3.cpp
index 8586f35a0..55720abca 100644
--- a/gtsam/geometry/tests/testPose3.cpp
+++ b/gtsam/geometry/tests/testPose3.cpp
@@ -818,6 +818,15 @@ TEST( Pose3, LogmapDerivative) {
   EXPECT(assert_equal(expectedH, actualH));
 }
 
+TEST( Pose3, computeQforExpmapDerivative) {
+  Vector6 w = Vector6::Random();
+  w.head<3>().normalize();
+  w.head<3>() = w.head<3>() * 0.09;
+  Matrix3 Qexact = Pose3::computeQforExpmapDerivative(w);
+  Matrix3 Qapprox = Pose3::computeQforExpmapDerivative(w, 0.1);
+  EXPECT(assert_equal(Qapprox, Qexact, 1e-5));
+}
+
 /* ************************************************************************* */
 Vector6 testDerivAdjoint(const Vector6& xi, const Vector6& v) {
   return Pose3::adjointMap(xi) * v;