diff --git a/gtsam/linear/NoiseModel.cpp b/gtsam/linear/NoiseModel.cpp
index 4d9c7883b..1569f61da 100644
--- a/gtsam/linear/NoiseModel.cpp
+++ b/gtsam/linear/NoiseModel.cpp
@@ -833,11 +833,10 @@ GemanMcClure::GemanMcClure(double c, const ReweightScheme reweight)
   : Base(reweight), c_(c) {
 }
 
-double GemanMcClure::weight(double error) const {
+double GemanMcClure::sqrtWeight(double error) const {
   const double c2 = c_*c_;
-  const double c4 = c2*c2;
   const double c2error = c2 + error*error;
-  return c4/(c2error*c2error);
+  return c2/c2error;
 }
 
 void GemanMcClure::print(const std::string &s="") const {
@@ -861,12 +860,12 @@ DCS::DCS(double c, const ReweightScheme reweight)
   : Base(reweight), c_(c) {
 }
 
-double DCS::weight(double error) const {
+double DCS::sqrtWeight(double error) const {
   const double e2 = error*error;
   if (e2 > c_)
   {
     const double w = 2.0*c_/(c_ + e2);
-    return w*w;
+    return w;
   }
 
   return 1.0;
diff --git a/gtsam/linear/NoiseModel.h b/gtsam/linear/NoiseModel.h
index e495921c2..b1e7d562a 100644
--- a/gtsam/linear/NoiseModel.h
+++ b/gtsam/linear/NoiseModel.h
@@ -661,6 +661,7 @@ namespace gtsam {
       public:
         Base(const ReweightScheme reweight = Block):reweight_(reweight) {}
         virtual ~Base() {}
+        ReweightScheme reweightScheme() const { return reweight_; }
 
         /*
          * This method is responsible for returning the total penalty for a given amount of error.
@@ -685,14 +686,14 @@ namespace gtsam {
          * for details. This method is required when optimizing cost functions with robust penalties
          * using iteratively re-weighted least squares.
          */
-        virtual double weight(double error) const = 0;
+        double weight(double error) const {
+          return sqrtWeight(error)*sqrtWeight(error);
+        }
 
         virtual void print(const std::string &s) const = 0;
         virtual bool equals(const Base& expected, double tol=1e-8) const = 0;
 
-        double sqrtWeight(double error) const {
-          return std::sqrt(weight(error));
-        }
+        virtual double sqrtWeight(double error) const = 0;
 
         /** produce a weight vector according to an error vector and the implemented
         * robust function */
@@ -726,7 +727,7 @@ namespace gtsam {
 
         Null(const ReweightScheme reweight = Block) : Base(reweight) {}
         virtual ~Null() {}
-        virtual double weight(double /*error*/) const { return 1.0; }
+        virtual double sqrtWeight(double /*error*/) const { return 1.0; }
         virtual void print(const std::string &s) const;
         virtual bool equals(const Base& /*expected*/, double /*tol*/) const { return true; }
         static shared_ptr Create() ;
@@ -749,8 +750,8 @@ namespace gtsam {
         typedef boost::shared_ptr<Fair> shared_ptr;
 
         Fair(double c = 1.3998, const ReweightScheme reweight = Block);
-        double weight(double error) const {
-          return 1.0 / (1.0 + fabs(error) / c_);
+        double sqrtWeight(double error) const {
+          return 1.0 / sqrt(1.0 + fabs(error) / c_);
         }
         void print(const std::string &s) const;
         bool equals(const Base& expected, double tol=1e-8) const;
@@ -775,8 +776,8 @@ namespace gtsam {
         typedef boost::shared_ptr<Huber> shared_ptr;
 
         Huber(double k = 1.345, const ReweightScheme reweight = Block);
-        double weight(double error) const {
-          return (error < k_) ? (1.0) : (k_ / fabs(error));
+        double sqrtWeight(double error) const {
+          return (error < k_) ? (1.0) : sqrt(k_ / fabs(error));
         }
         void print(const std::string &s) const;
         bool equals(const Base& expected, double tol=1e-8) const;
@@ -805,8 +806,8 @@ namespace gtsam {
         typedef boost::shared_ptr<Cauchy> shared_ptr;
 
         Cauchy(double k = 0.1, const ReweightScheme reweight = Block);
-        double weight(double error) const {
-          return ksquared_ / (ksquared_ + error*error);
+        double sqrtWeight(double error) const {
+          return k_ / sqrt(ksquared_ + error*error);
         }
         void print(const std::string &s) const;
         bool equals(const Base& expected, double tol=1e-8) const;
@@ -831,10 +832,10 @@ namespace gtsam {
         typedef boost::shared_ptr<Tukey> shared_ptr;
 
         Tukey(double c = 4.6851, const ReweightScheme reweight = Block);
-        double weight(double error) const {
+        double sqrtWeight(double error) const {
           if (std::fabs(error) <= c_) {
             double xc2 = error*error/csquared_;
-            return (1.0-xc2)*(1.0-xc2);
+            return (1.0-xc2);
           }
           return 0.0;
         }
@@ -861,9 +862,9 @@ namespace gtsam {
         typedef boost::shared_ptr<Welsh> shared_ptr;
 
         Welsh(double c = 2.9846, const ReweightScheme reweight = Block);
-        double weight(double error) const {
+        double sqrtWeight(double error) const {
           double xc2 = (error*error)/csquared_;
-          return std::exp(-xc2);
+          return std::exp(-xc2/2.0);
         }
         void print(const std::string &s) const;
         bool equals(const Base& expected, double tol=1e-8) const;
@@ -891,7 +892,7 @@ namespace gtsam {
 
         GemanMcClure(double c = 1.0, const ReweightScheme reweight = Block);
         virtual ~GemanMcClure() {}
-        virtual double weight(double error) const;
+        virtual double sqrtWeight(double error) const;
         virtual void print(const std::string &s) const;
         virtual bool equals(const Base& expected, double tol=1e-8) const;
         static shared_ptr Create(double k, const ReweightScheme reweight = Block) ;
@@ -920,7 +921,7 @@ namespace gtsam {
 
         DCS(double c = 1.0, const ReweightScheme reweight = Block);
         virtual ~DCS() {}
-        virtual double weight(double error) const;
+        virtual double sqrtWeight(double error) const;
         virtual void print(const std::string &s) const;
         virtual bool equals(const Base& expected, double tol=1e-8) const;
         static shared_ptr Create(double k, const ReweightScheme reweight = Block) ;
@@ -955,13 +956,13 @@ namespace gtsam {
             const double abs_error = fabs(error);
             return (abs_error < k_) ? 0.0 : 0.5*(k_-abs_error)*(k_-abs_error);
           }
-          double weight(double error) const {
+          double sqrtWeight(double error) const {
             // note that this code is slightly uglier than above, because there are three distinct
             // cases to handle (left of deadzone, deadzone, right of deadzone) instead of the two
             // cases (deadzone, non-deadzone) above.
             if (fabs(error) <= k_) return 0.0;
-            else if (error > k_) return (-k_+error)/error;
-            else return (k_+error)/error;
+            else if (error > k_) return sqrt((-k_+error)/error);
+            else return sqrt((k_+error)/error);
           }
           void print(const std::string &s) const;
           bool equals(const Base& expected, double tol=1e-8) const;