diff --git a/Tests/Data/ThermoHydroMechanics/RestartMCC/mfront_restart_part1.prj b/Tests/Data/ThermoHydroMechanics/RestartMCC/mfront_restart_part1.prj
index d9a785078df1907b77ce29d83da04966c5023268..c11c1c60a02dea44b706393f3743241e559b8b26 100644
--- a/Tests/Data/ThermoHydroMechanics/RestartMCC/mfront_restart_part1.prj
+++ b/Tests/Data/ThermoHydroMechanics/RestartMCC/mfront_restart_part1.prj
@@ -1,4 +1,5 @@
 <?xml version="1.0" encoding="ISO-8859-1"?>
+<!--oedometer-type test with MCC behavior, stress-controlled plastic loading-->
 <OpenGeoSysProject>
     <meshes>
         <mesh axially_symmetric="true">square_1x1_quad_1e0.vtu</mesh>
@@ -304,7 +305,7 @@
         <nonlinear_solver>
             <name>basic_newton</name>
             <type>Newton</type>
-            <max_iter>60</max_iter>
+            <max_iter>20</max_iter>
             <linear_solver>general_linear_solver</linear_solver>
         </nonlinear_solver>
     </nonlinear_solvers>
@@ -322,7 +323,7 @@
         <vtkdiff>
             <regex>mfront_restart_part1_t_.*.vtu</regex>
             <field>pressure</field>
-            <absolute_tolerance>1e-15</absolute_tolerance>
+            <absolute_tolerance>5e-11</absolute_tolerance>
             <relative_tolerance>0</relative_tolerance>
         </vtkdiff>
         <vtkdiff>
@@ -335,7 +336,7 @@
         <vtkdiff>
             <regex>mfront_restart_part1_t_.*.vtu</regex>
             <field>sigma</field>
-            <absolute_tolerance>3e-10</absolute_tolerance>
+            <absolute_tolerance>1e-9</absolute_tolerance>
             <relative_tolerance>0</relative_tolerance>
         </vtkdiff>
         <vtkdiff>
@@ -353,7 +354,7 @@
         <vtkdiff>
             <regex>mfront_restart_part1_t_.*.vtu</regex>
             <field>NodalForces</field>
-            <absolute_tolerance>1e-12</absolute_tolerance>
+            <absolute_tolerance>1e-9</absolute_tolerance>
             <relative_tolerance>0</relative_tolerance>
         </vtkdiff>
         <!--internal state variables-->
@@ -366,14 +367,14 @@
         <vtkdiff>
             <regex>mfront_restart_part1_t_.*.vtu</regex>
             <field>PreConsolidationPressure</field>
-            <absolute_tolerance>6e-11</absolute_tolerance>
+            <absolute_tolerance>7e-10</absolute_tolerance>
             <relative_tolerance>0</relative_tolerance>
             </vtkdiff>
         <!--integration point variables-->
         <vtkdiff>
             <regex>mfront_restart_part1_t_.*.vtu</regex>
             <field>sigma_ip</field>
-            <absolute_tolerance>1e-14</absolute_tolerance>
+            <absolute_tolerance>3e-10</absolute_tolerance>
             <relative_tolerance>0</relative_tolerance>
         </vtkdiff>
         <vtkdiff>
diff --git a/Tests/Data/ThermoHydroMechanics/RestartMCC/mfront_restart_part2.xml b/Tests/Data/ThermoHydroMechanics/RestartMCC/mfront_restart_part2.xml
index 68f33fa990d3d426a0b18fd6fdba94736786d95b..4491ffb9d284c009813f933538e05efef29e3139 100644
--- a/Tests/Data/ThermoHydroMechanics/RestartMCC/mfront_restart_part2.xml
+++ b/Tests/Data/ThermoHydroMechanics/RestartMCC/mfront_restart_part2.xml
@@ -1,4 +1,5 @@
 <?xml version="1.0" encoding="ISO-8859-1"?>
+<!--oedometer-type test with MCC behavior, restart with hydraulic unloading and plastic response-->
 <OpenGeoSysProjectDiff base_file="mfront_restart_part1.prj">
     <replace sel="/*/meshes/mesh[1]/text()">mfront_restart_part1_t_1000.000000.vtu</replace>
     <replace sel="/*/time_loop/processes/process/time_stepping/t_initial/text()">1000</replace>
@@ -49,7 +50,7 @@
         <vtkdiff>
             <regex>mfront_restart_part2_t_.*.vtu</regex>
             <field>pressure</field>
-            <absolute_tolerance>1e-15</absolute_tolerance>
+            <absolute_tolerance>6e-11</absolute_tolerance>
             <relative_tolerance>0</relative_tolerance>
         </vtkdiff>
         <vtkdiff>
@@ -62,7 +63,7 @@
         <vtkdiff>
             <regex>mfront_restart_part2_t_.*.vtu</regex>
             <field>sigma</field>
-            <absolute_tolerance>3e-10</absolute_tolerance>
+            <absolute_tolerance>3e-9</absolute_tolerance>
             <relative_tolerance>0</relative_tolerance>
         </vtkdiff>
         <vtkdiff>
@@ -80,7 +81,7 @@
         <vtkdiff>
             <regex>mfront_restart_part2_t_.*.vtu</regex>
             <field>NodalForces</field>
-            <absolute_tolerance>1e-12</absolute_tolerance>
+            <absolute_tolerance>2e-9</absolute_tolerance>
             <relative_tolerance>0</relative_tolerance>
         </vtkdiff>
         <!--internal state variables-->
@@ -93,14 +94,14 @@
         <vtkdiff>
             <regex>mfront_restart_part2_t_.*.vtu</regex>
             <field>PreConsolidationPressure</field>
-            <absolute_tolerance>3e-10</absolute_tolerance>
+            <absolute_tolerance>1e-9</absolute_tolerance>
             <relative_tolerance>0</relative_tolerance>
             </vtkdiff>
         <!--integration point variables-->
         <vtkdiff>
             <regex>mfront_restart_part2_t_.*.vtu</regex>
             <field>sigma_ip</field>
-            <absolute_tolerance>1e-14</absolute_tolerance>
+            <absolute_tolerance>2e-9</absolute_tolerance>
             <relative_tolerance>0</relative_tolerance>
         </vtkdiff>
         <vtkdiff>