diff --git a/gtsam/geometry/SO3.cpp b/gtsam/geometry/SO3.cpp
index a03ff7648..c86b9b860 100644
--- a/gtsam/geometry/SO3.cpp
+++ b/gtsam/geometry/SO3.cpp
@@ -262,12 +262,12 @@ Vector3 SO3::Logmap(const SO3& Q, ChartJacobian H) {
   // when trace == -1, i.e., when theta = +-pi, +-3pi, +-5pi, etc.
   // we do something special
   if (tr + 1.0 < 1e-10) {
-    if (std::abs(R33 + 1.0) > 1e-10)
+    if (std::abs(R33 + 1.0) > 1e-5)
       omega = (M_PI / sqrt(2.0 + 2.0 * R33)) * Vector3(R13, R23, 1.0 + R33);
-    else if (std::abs(R22 + 1.0) > 1e-10)
+    else if (std::abs(R22 + 1.0) > 1e-5)
       omega = (M_PI / sqrt(2.0 + 2.0 * R22)) * Vector3(R12, 1.0 + R22, R32);
     else
-      // if(std::abs(R.r1_.x()+1.0) > 1e-10)  This is implicit
+      // if(std::abs(R.r1_.x()+1.0) > 1e-5)  This is implicit
       omega = (M_PI / sqrt(2.0 + 2.0 * R11)) * Vector3(1.0 + R11, R21, R31);
   } else {
     double magnitude;
diff --git a/gtsam/geometry/tests/testRot3.cpp b/gtsam/geometry/tests/testRot3.cpp
index 74fa829d8..19d696abd 100644
--- a/gtsam/geometry/tests/testRot3.cpp
+++ b/gtsam/geometry/tests/testRot3.cpp
@@ -243,8 +243,13 @@ TEST(Rot3, log) {
   Rot3 Rlund(-0.98582676, -0.03958746, -0.16303092,  //
              -0.03997006, -0.88835923, 0.45740671,   //
              -0.16293753, 0.45743998, 0.87418537);
-  EXPECT(assert_equal(Vector3(-0.264544406, 0.742217405, 3.04117314),
-                      (Vector)Rot3::Logmap(Rlund), 1e-8));
+  #if defined(GTSAM_USE_QUATERNIONS)
+    EXPECT(assert_equal(Vector3(0.264451979, -0.742197651, -3.04098211),
+                        (Vector)Rot3::Logmap(Rlund), 1e-8));
+  #else
+    EXPECT(assert_equal(Vector3(-0.264544406, 0.742217405, 3.04117314),
+                        (Vector)Rot3::Logmap(Rlund), 1e-8));
+  #endif
 }
 
 /* ************************************************************************* */