diff --git a/tst/canonical-grp-3.tst b/tst/canonical-grp-3.tst
new file mode 100644
index 0000000..d62e372
--- /dev/null
+++ b/tst/canonical-grp-3.tst
@@ -0,0 +1,18 @@
+#@local
+gap> START_TEST("canonical-grp-3.tst");
+gap> ReadPackage("vole", "tst/test_functions.g");
+true
+
+#
+gap> QC_Check([IsPermGroup, IsPermGroup],
+> function(g,s)
+>   local lmp;
+>   lmp := Maximum(LargestMovedPoint(g), LargestMovedPoint(s), 2);
+>   return VoleTestCanonical(lmp, g, s,
+>     {x} -> [VoleCon.Stabilize(x)],
+>     {x,p} -> x^p);
+> end);
+true
+
+#
+gap> STOP_TEST("canonical-grp-3.tst");
diff --git a/tst/canonical-grp-4.tst b/tst/canonical-grp-4.tst
new file mode 100644
index 0000000..b581bfb
--- /dev/null
+++ b/tst/canonical-grp-4.tst
@@ -0,0 +1,18 @@
+#@local
+gap> START_TEST("canonical-grp-4.tst");
+gap> ReadPackage("vole", "tst/test_functions.g");
+true
+
+#
+gap> QC_Check([IsPermGroup],
+> function(s)
+>   local lmp;
+>   lmp := Maximum( LargestMovedPoint(s), 2);
+>   return VoleTestCanonical(lmp, SymmetricGroup(lmp), s,
+>     {x} -> [VoleCon.Stabilize(x)],
+>     {x,p} -> x^p);
+> end);
+true
+
+#
+gap> STOP_TEST("canonical-grp-4.tst");