diff --git a/gtsam/base/cholesky.cpp b/gtsam/base/cholesky.cpp
index d5b69a25f..9585d024b 100644
--- a/gtsam/base/cholesky.cpp
+++ b/gtsam/base/cholesky.cpp
@@ -33,8 +33,8 @@ using namespace std;
 namespace gtsam {
 
   static const double negativePivotThreshold = -1e-1;
-  static const double zeroPivotThreshold = 1e-3;
-  static const double underconstrainedPrior = 0.001;
+  static const double zeroPivotThreshold = 1e-6;
+  static const double underconstrainedPrior = 1e-5;
 
 /* ************************************************************************* */
 void cholesky_inplace(MatrixColMajor& I) {