diff --git a/docs/api.tex b/docs/api.tex
index c8feeeb..471f2de 100644
--- a/docs/api.tex
+++ b/docs/api.tex
@@ -462,6 +462,16 @@
 
 \item{\texttt{tau}}(\texttt{1e-4}) Initial value of the regularization parameter $\mu$ used by the Levenberg-Marquardt algorithm. The size of this parameter indicate the user's guess of how far the initial solution is from the minimum. Large values indicates that the solution is far away.
 
+\item{\texttt{min\_mu}(\texttt{1e-20})} For Levenberg-Marquardt, the minimum value of the
+     regularizer. For well constrained problems there shold be no
+     need to modify the default value, but in some cases, going
+     below a certain minimum reliably triggers rank deficiency in
+     the normal equations. In such cases, the Levenberg-Marquardt algorithm can
+     oscillate between lowering the value of mu, seeing a numerical
+     failure, and then increasing it making some progress and then
+     reducing it again.
+    
+     In such cases, it is useful to set a higher value for \texttt{min\_mu}.
 \item{\texttt{min\_relative\_decrease}}(\texttt{1e-3}) Lower threshold for relative decrease before a Levenberg-Marquardt step is acceped.
 
 
diff --git a/include/ceres/solver.h b/include/ceres/solver.h
index bd66927..be81768 100644
--- a/include/ceres/solver.h
+++ b/include/ceres/solver.h
@@ -62,6 +62,7 @@
       max_solver_time_sec = 1.0e9;
       num_threads = 1;
       tau = 1e-4;
+      min_mu = 1e-20;
       min_relative_decrease = 1e-3;
       function_tolerance = 1e-6;
       gradient_tolerance = 1e-10;
@@ -111,6 +112,18 @@
     // initial trust region.
     double tau;
 
+    // For Levenberg-Marquardt, the minimum value of the
+    // regularizer. For well constrained problems there shold be no
+    // need to modify the default value, but in some cases, going
+    // below a certain minimum reliably triggers rank deficiency in
+    // the normal equations. In such cases, the LM solver can
+    // oscillate between lowering the value of mu, seeing a numerical
+    // failure, and then increasing it making some progress and then
+    // reducing it again.
+    //
+    // In such cases, it is useful to set a higher value for min_mu.
+    double min_mu;
+
     // For trust region methods, this is lower threshold for the
     // relative decrease before a step is accepted.
     double min_relative_decrease;
diff --git a/internal/ceres/levenberg_marquardt.cc b/internal/ceres/levenberg_marquardt.cc
index 7d3afac..1eae624 100644
--- a/internal/ceres/levenberg_marquardt.cc
+++ b/internal/ceres/levenberg_marquardt.cc
@@ -498,6 +498,7 @@
       }
 
       mu = mu * max(1.0 / 3.0, 1 - pow(2 * relative_decrease - 1, 3));
+      mu = std::max(options.min_mu, mu);
       nu = 2.0;
       step_is_successful = true;
       break;
diff --git a/internal/ceres/minimizer.h b/internal/ceres/minimizer.h
index 77cb00c..19b0344 100644
--- a/internal/ceres/minimizer.h
+++ b/internal/ceres/minimizer.h
@@ -57,6 +57,7 @@
       min_relative_decrease = options.min_relative_decrease;
       eta = options.eta;
       tau = options.tau;
+      min_mu = options.min_mu;
       jacobi_scaling = options.jacobi_scaling;
       crash_and_dump_lsqp_on_failure = options.crash_and_dump_lsqp_on_failure;
       lsqp_dump_directory = options.lsqp_dump_directory;
@@ -74,6 +75,7 @@
     double min_relative_decrease;
     double eta;
     double tau;
+    double min_mu;
     bool jacobi_scaling;
     bool crash_and_dump_lsqp_on_failure;
     vector<int> lsqp_iterations_to_dump;