diff --git a/compareECLFiles.cmake b/compareECLFiles.cmake
index 711c0af52..007a9bd7f 100755
--- a/compareECLFiles.cmake
+++ b/compareECLFiles.cmake
@@ -764,7 +764,7 @@ opm_set_test_driver(${PROJECT_SOURCE_DIR}/tests/run-restart-regressionTest.sh ""
 
 # Cruder tolerances for the restarted tests
 set(abs_tol_restart 2e-1)
-set(rel_tol_restart 4e-5)
+set(rel_tol_restart 5e-5)
 
 add_test_compare_restarted_simulation(CASENAME spe1
                                       FILENAME SPE1CASE2_ACTNUM
@@ -829,7 +829,7 @@ if(MPI_FOUND)
 
   # Different tolerances for these tests
   set(abs_tol_parallel 0.02)
-  set(rel_tol_parallel 1e-5)
+  set(rel_tol_parallel 8e-5)
   set(coarse_rel_tol_parallel 1e-2)
 
   add_test_compare_parallel_simulation(CASENAME spe1