diff --git a/README.md b/README.md
index 131c46c48346f420f1089850c26eec26bdbeb8b3..d494ed10ac250aeeecdcbd8a61b53b623028736e 100644
--- a/README.md
+++ b/README.md
@@ -51,7 +51,7 @@ This is an up to date list of available keyword options:
   - `store_overlap`:  bool, default True. Store the overlaps for later usage in calling guess without passing the current overlap. It can be disabled for performance, but calling guess will require passing the overlap.
 
 Some options can be piped to the fitting modules.
-  - `fitting_regularization`: float, default 0.0. Controls the regularization for both the "leastsquare" and "qtr" fitting schemes. In both the fitting schemes, an additional term of the form $\varepsilon^2 ||\alpha||^2$ is added to the error function, in this expression $\alpha$ is the vector of coefficients and $\varepsilon$ is the regularization.
+  - `fitting_regularization`: float, default 0.001. Controls the regularization for both the "leastsquare" and "qtr" fitting schemes. In both the fitting schemes, an additional term of the form $\varepsilon^2 ||\alpha||^2$ is added to the error function, in this expression $\alpha$ is the vector of coefficients and $\varepsilon$ is the regularization.
 
 
 ## Acknowledgments
diff --git a/gext/fitting.py b/gext/fitting.py
index 21fa5a36b2ce4655b5aeba527433cd653007f9e8..d9b7997a4d0c90a371bdf732205f382e4aac8af1 100644
--- a/gext/fitting.py
+++ b/gext/fitting.py
@@ -46,7 +46,7 @@ class LeastSquare(AbstractFitting):
     """Simple least square minimization fitting."""
 
     supported_options = {
-        "regularization": 0.0,
+        "regularization": 1e-3,
     }
 
     def set_options(self, **kwargs):
@@ -73,7 +73,7 @@ class QuasiTimeReversible(AbstractFitting):
     """Quasi time reversible fitting scheme."""
 
     supported_options = {
-        "regularization": 0.0,
+        "regularization": 1e-3,
     }
 
     def set_options(self, **kwargs):