diff --git a/gtsam/linear/GaussianConditional.cpp b/gtsam/linear/GaussianConditional.cpp
index 6a6f75d73..21787ba7d 100644
--- a/gtsam/linear/GaussianConditional.cpp
+++ b/gtsam/linear/GaussianConditional.cpp
@@ -63,10 +63,11 @@ namespace gtsam {
   GaussianConditional GaussianConditional::FromMeanAndStddev(
       Key key, const Matrix& A, Key parent, const Vector& b, double sigma) {
     // |Rx + Sy - d| = |x-(Ay + b)|/sigma
-    const Matrix R = Matrix::Identity(b.size(), b.size()) / sigma;
-    const Matrix S = -A / sigma;
-    const Vector d = b / sigma;
-    return GaussianConditional(key, d, R, parent, S);
+    const Matrix R = Matrix::Identity(b.size(), b.size());
+    const Matrix S = -A;
+    const Vector d = b;
+    return GaussianConditional(key, d, R, parent, S,
+                               noiseModel::Isotropic::Sigma(b.size(), sigma));
   }
 
   /* ************************************************************************ */
@@ -74,11 +75,12 @@ namespace gtsam {
       Key key, const Matrix& A1, Key parent1, const Matrix& A2, Key parent2,
       const Vector& b, double sigma) {
     // |Rx + Sy + Tz - d| = |x-(A1 y + A2 z + b)|/sigma
-    const Matrix R = Matrix::Identity(b.size(), b.size()) / sigma;
-    const Matrix S = -A1 / sigma;
-    const Matrix T = -A2 / sigma;
-    const Vector d = b / sigma;
-    return GaussianConditional(key, d, R, parent1, S, parent2, T);
+    const Matrix R = Matrix::Identity(b.size(), b.size());
+    const Matrix S = -A1;
+    const Matrix T = -A2;
+    const Vector d = b;
+    return GaussianConditional(key, d, R, parent1, S, parent2, T,
+                               noiseModel::Isotropic::Sigma(b.size(), sigma));
   }
 
   /* ************************************************************************ */
diff --git a/gtsam/linear/GaussianDensity.cpp b/gtsam/linear/GaussianDensity.cpp
index 2bae129be..2f7aa312b 100644
--- a/gtsam/linear/GaussianDensity.cpp
+++ b/gtsam/linear/GaussianDensity.cpp
@@ -26,8 +26,9 @@ namespace gtsam {
   GaussianDensity GaussianDensity::FromMeanAndStddev(Key key,
                                                      const Vector& mean,
                                                      double sigma) {
-    return GaussianDensity(key, mean / sigma,
-                           Matrix::Identity(mean.size(), mean.size()) / sigma);
+    return GaussianDensity(key, mean,
+                           Matrix::Identity(mean.size(), mean.size()),
+                           noiseModel::Isotropic::Sigma(mean.size(), sigma));
   }
 
   /* ************************************************************************* */
diff --git a/gtsam/linear/tests/testGaussianDensity.cpp b/gtsam/linear/tests/testGaussianDensity.cpp
index 29dc49591..14608e794 100644
--- a/gtsam/linear/tests/testGaussianDensity.cpp
+++ b/gtsam/linear/tests/testGaussianDensity.cpp
@@ -17,10 +17,13 @@
  **/
 
 #include <gtsam/linear/GaussianDensity.h>
+#include <gtsam/inference/Symbol.h>
+
 #include <CppUnitLite/TestHarness.h>
 
 using namespace gtsam;
 using namespace std;
+using symbol_shorthand::X;
 
 /* ************************************************************************* */
 TEST(GaussianDensity, constructor)
@@ -37,6 +40,22 @@ TEST(GaussianDensity, constructor)
   EXPECT(assert_equal(s, copied.get_model()->sigmas()));
 }
 
+/* ************************************************************************* */
+// Test FromMeanAndStddev named constructor
+TEST(GaussianDensity, FromMeanAndStddev) {
+  Matrix A1 = (Matrix(2, 2) << 1., 2., 3., 4.).finished();
+  const Vector2 b(20, 40), x0(1, 2);
+  const double sigma = 3;
+
+  VectorValues values;
+  values.insert(X(0), x0);
+
+  auto density = GaussianDensity::FromMeanAndStddev(X(0), b, sigma);
+  Vector2 e = (x0 - b) / sigma;
+  double expected = 0.5 * e.dot(e);
+  EXPECT_DOUBLES_EQUAL(expected, density.error(values), 1e-9);
+}
+
 /* ************************************************************************* */
 int main() { TestResult tr; return TestRegistry::runAllTests(tr);}
 /* ************************************************************************* */