diff --git a/gtsam/linear/HessianFactor.cpp b/gtsam/linear/HessianFactor.cpp
index 72503b470..5baee8712 100644
--- a/gtsam/linear/HessianFactor.cpp
+++ b/gtsam/linear/HessianFactor.cpp
@@ -254,10 +254,10 @@ HessianFactor::HessianFactor(const GaussianFactor& gf) : info_(matrix_) {
     if(jf.model_->isConstrained())
       throw invalid_argument("Cannot construct HessianFactor from JacobianFactor with constrained noise model");
     else {
-      Vector invsigmas = jf.model_->invsigmas().cwiseProduct(jf.model_->invsigmas());
+      const Vector& precisions = jf.model_->precisions();
       info_.copyStructureFrom(jf.Ab_);
       BlockInfo::constBlock A = jf.Ab_.full();
-      matrix_.noalias() = A.transpose() * invsigmas.asDiagonal() * A;
+      matrix_.noalias() = A.transpose() * precisions.asDiagonal() * A;
     }
   } else if(dynamic_cast<const HessianFactor*>(&gf)) {
     const HessianFactor& hf(static_cast<const HessianFactor&>(gf));
diff --git a/gtsam/linear/NoiseModel.cpp b/gtsam/linear/NoiseModel.cpp
index 88b57046e..16b0a5bc1 100644
--- a/gtsam/linear/NoiseModel.cpp
+++ b/gtsam/linear/NoiseModel.cpp
@@ -308,8 +308,6 @@ SharedDiagonal Constrained::QR(Matrix& Ab) const {
   list<Triple> Rd;
 
   Vector pseudo(m); // allocate storage for pseudo-inverse
-  Vector invsigmas = reciprocal(sigmas_);
-  Vector weights = emul(invsigmas,invsigmas); // calculate weights once
 
   // We loop over all columns, because the columns that can be eliminated
   // are not necessarily contiguous. For each one, estimate the corresponding
@@ -321,7 +319,7 @@ SharedDiagonal Constrained::QR(Matrix& Ab) const {
 
     // Calculate weighted pseudo-inverse and corresponding precision
     gttic(constrained_QR_weightedPseudoinverse);
-    double precision = weightedPseudoinverse(a, weights, pseudo);
+    double precision = weightedPseudoinverse(a, precisions_, pseudo);
     gttoc(constrained_QR_weightedPseudoinverse);
 
     // If precision is zero, no information on this column
diff --git a/gtsam/linear/NoiseModel.h b/gtsam/linear/NoiseModel.h
index 704106bc8..37e5f0090 100644
--- a/gtsam/linear/NoiseModel.h
+++ b/gtsam/linear/NoiseModel.h
@@ -342,11 +342,9 @@ namespace gtsam {
       Vector mu_;
 
       /** protected constructor takes sigmas */
-      // Keeps only sigmas and calculates invsigmas when necessary
       Constrained(const Vector& sigmas = zero(1)) :
         Diagonal(sigmas), mu_(repeat(sigmas.size(), 1000.0)) {}
 
-      // Keeps only sigmas and calculates invsigmas when necessary
       // allows for specifying mu
       Constrained(const Vector& mu, const Vector& sigmas) :
         Diagonal(sigmas), mu_(mu) {}