diff --git a/gtsam/nonlinear/GncOptimizer.h b/gtsam/nonlinear/GncOptimizer.h
index be7d046c6..b6e6933ec 100644
--- a/gtsam/nonlinear/GncOptimizer.h
+++ b/gtsam/nonlinear/GncOptimizer.h
@@ -65,6 +65,7 @@ public:
   size_t maxIterations = 100; /* maximum number of iterations*/
   double barcSq = 1.0; /* a factor is considered an inlier if factor.error() < barcSq. Note that factor.error() whitens by the covariance*/
   double muStep = 1.4; /* multiplicative factor to reduce/increase the mu in gnc */
+  double relativeMuTol = 1e-5; ///< The maximum relative mu decrease to stop iterating
   VerbosityGNC verbosityGNC = SILENT; /* verbosity level */
   std::vector<size_t> knownInliers = std::vector<size_t>(); /* slots in the factor graph corresponding to measurements that we know are inliers */
 
@@ -89,6 +90,10 @@ public:
   void setMuStep(const double step) {
     muStep = step;
   }
+  /// Set the maximum relative difference in mu values to stop iterating
+  void setRelativeMuTol(double value) {
+    relativeMuTol = value;
+  }
   /// Set the verbosity level
   void setVerbosityGNC(const VerbosityGNC verbosity) {
     verbosityGNC = verbosity;
@@ -196,6 +201,7 @@ public:
     GaussNewtonOptimizer baseOptimizer(nfg_, state_);
     Values result = baseOptimizer.optimize();
     double mu = initializeMu();
+    double mu_prev = mu;
 
     // handle the degenerate case for TLS cost that corresponds to small
     // maximum residual error at initialization
@@ -225,7 +231,7 @@ public:
       result = baseOptimizer_iter.optimize();
 
       // stopping condition
-      if (checkMuConvergence(mu)) {
+      if (checkMuConvergence(mu, mu_prev)) {
         // display info
         if (params_.verbosityGNC >= GncParameters::VerbosityGNC::SUMMARY) {
           std::cout << "final iterations: " << iter << std::endl;
@@ -235,6 +241,7 @@ public:
         break;
       }
       // otherwise update mu
+      mu_prev = mu;
       mu = updateMu(mu);
     }
     return result;
@@ -279,11 +286,12 @@ public:
   }
 
   /// check if we have reached the value of mu for which the surrogate loss matches the original loss
-  bool checkMuConvergence(const double mu) const {
+  bool checkMuConvergence(const double mu, const double mu_prev) const {
     switch (params_.lossType) {
     case GncParameters::GM:
       return std::fabs(mu - 1.0) < 1e-9; // mu=1 recovers the original GM function
-      // TODO: Add TLS
+    case GncParameters::TLS:
+      return std::fabs(mu - mu_prev) < params_.relativeMuTol;
     default:
       throw std::runtime_error(
           "GncOptimizer::checkMuConvergence: called with unknown loss type.");
@@ -341,7 +349,22 @@ public:
         }
       }
       return weights;
-      // TODO: Add TLS
+    case GncParameters::TLS: // use eq (14) in GNC paper
+      double upperbound = (mu + 1) / mu * params_.barcSq;
+      double lowerbound = mu / (mu +1 ) * params_.barcSq;
+      for (size_t k : unknownWeights) {
+        if (nfg_[k]) {
+          double u2_k = nfg_[k]->error(currentEstimate); // squared (and whitened) residual
+          if (u2_k >= upperbound ) {
+            weights[k] = 0;
+          } else if (u2_k <= lowerbound) {
+            weights[k] = 1;
+          } else {
+            weights[k] = std::sqrt(params_.barcSq * mu * (mu + 1) / u2_k ) - mu;
+          }
+        }
+      }
+      return weights;
     default:
       throw std::runtime_error(
           "GncOptimizer::calculateWeights: called with unknown loss type.");
diff --git a/tests/testGncOptimizer.cpp b/tests/testGncOptimizer.cpp
index 5006aa941..3f784b96e 100644
--- a/tests/testGncOptimizer.cpp
+++ b/tests/testGncOptimizer.cpp
@@ -162,7 +162,9 @@ TEST(GncOptimizer, checkMuConvergence) {
       gncParams);
 
   double mu = 1.0;
-  CHECK(gnc.checkMuConvergence(mu));
+  CHECK(gnc.checkMuConvergence(mu, 0));
+
+  // TODO: test relative mu convergence
 }
 
 /* ************************************************************************* */