diff --git a/lib/profile.g b/lib/profile.g
index 6972bc0e3f..ca7d399c09 100644
--- a/lib/profile.g
+++ b/lib/profile.g
@@ -1068,9 +1068,6 @@ end);
 ##  <Log><![CDATA[
 ##  gap> STOP_TEST( "same identifier string as for START_TEST" );
 ##  ]]></Log>
-##  <P/>
-##  Note that the functions in <F>tst/testutil.g</F> temporarily replace
-##  <Ref Func="STOP_TEST"/> before they call <Ref Func="Test"/>.
 ##  </Description>
 ##  </ManSection>
 ##  <#/GAPDoc>
diff --git a/tst/testutil.g b/tst/delegation.g
similarity index 96%
rename from tst/testutil.g
rename to tst/delegation.g
index 2c96fd24bf..e8dee4758c 100644
--- a/tst/testutil.g
+++ b/tst/delegation.g
@@ -7,9 +7,6 @@
 ##
 ##  SPDX-License-Identifier: GPL-2.0-or-later
 ##
-##  This file contains utilities for running tests.
-##  It is not read with the library when {\GAP} is started.
-##
 
 
 #############################################################################
diff --git a/tst/test32bit/perm.tst b/tst/test32bit/perm.tst
deleted file mode 100644
index bc7c74d8e1..0000000000
--- a/tst/test32bit/perm.tst
+++ /dev/null
@@ -1,5 +0,0 @@
-#
-gap> f:={a,b} -> (a,b);;
-gap> f(2,2^40);
-Error, Permutation: <expr> must be a positive small integer (not a large posit\
-ive integer)
diff --git a/tst/test64bit/perm.tst b/tst/test64bit/perm.tst
deleted file mode 100644
index 2f05bc07f2..0000000000
--- a/tst/test64bit/perm.tst
+++ /dev/null
@@ -1,4 +0,0 @@
-#
-gap> f:={a,b} -> (a,b);;
-gap> f(2,2^40);
-Error, Permutation literal exceeds maximum permutation degree
diff --git a/tst/testbugfix/2005-05-05-t00072.tst b/tst/testbugfix/2005-05-05-t00072.tst
deleted file mode 100644
index f54159e435..0000000000
--- a/tst/testbugfix/2005-05-05-t00072.tst
+++ /dev/null
@@ -1,3 +0,0 @@
-# 2005/05/05 (TB)
-gap> IsReadableFile( Filename( DirectoriesLibrary( "tst" ), "testutil.g" ) );
-true
diff --git a/tst/testinstall/coll.tst b/tst/testinstall/coll.tst
index cdb2c3c87d..823517b148 100644
--- a/tst/testinstall/coll.tst
+++ b/tst/testinstall/coll.tst
@@ -4,7 +4,7 @@
 ##
 gap> START_TEST("coll.tst");
 gap> if not IsBound(TestConsistencyOfEnumeratorByFunctions) then
->   ReadGapRoot( "tst/testenumerator.g" );
+>   ReadGapRoot( "tst/testinstall/testenumerator.g" );
 > fi;
 
 #
diff --git a/tst/testinstall/perm.tst b/tst/testinstall/perm.tst
index 5431cc4a00..295af000f6 100644
--- a/tst/testinstall/perm.tst
+++ b/tst/testinstall/perm.tst
@@ -26,6 +26,13 @@ gap> (1,2)(1,2);
 Error, Permutation: cycles must be disjoint and duplicate-free
 gap> (1,2,3,2);
 Error, Permutation: cycles must be disjoint and duplicate-free
+gap> (1,2^80);
+Error, Permutation: <expr> must be a positive small integer (not a large posit\
+ive integer)
+#@if 8*GAPInfo.BytesPerVariable = 64
+gap> (1,2^40);
+Error, Permutation literal exceeds maximum permutation degree
+#@fi
 
 # The GAP kernel implements many functions in multiple variants, e.g. to
 # compare permutations for equality, there are actually four functions in the
diff --git a/tst/testinstall/random.tst b/tst/testinstall/random.tst
index eb30567a33..a3a5bd2a3e 100644
--- a/tst/testinstall/random.tst
+++ b/tst/testinstall/random.tst
@@ -1,6 +1,6 @@
 #@local R,a,rm,g,orbs,orb,i,getOneInt
 gap> START_TEST("random.tst");
-gap> ReadGapRoot( "tst/testrandom.g" );
+gap> ReadGapRoot( "tst/testinstall/testrandom.g" );
 
 # Test RandomList
 gap> randomTest([1,2,3], RandomList);
diff --git a/tst/testinstall/restrictedperm.tst b/tst/testinstall/restrictedperm.tst
index fc988f34ce..45a5cc1716 100644
--- a/tst/testinstall/restrictedperm.tst
+++ b/tst/testinstall/restrictedperm.tst
@@ -11,14 +11,6 @@ Error, <g> must be a permutation and <D> a plain list or range,
 gap> RestrictedPerm((),[ 1, 0 ]);
 Error, <g> must be a permutation and <D> a plain list or range,
    consisting of a union of cycles of <g>
-#@if 8*GAPInfo.BytesPerVariable = 64
-gap> RestrictedPerm((1,2^40),[ 1, () ]);
-Error, Permutation literal exceeds maximum permutation degree
-#@else
-gap> RestrictedPerm((1,2^40),[ 1, () ]);
-Error, Permutation: <expr> must be a positive small integer (not a large posit\
-ive integer)
-#@fi
 gap> RestrictedPerm((1,2^17),[ 1, () ]);
 Error, <g> must be a permutation and <D> a plain list or range,
    consisting of a union of cycles of <g>
diff --git a/tst/testenumerator.g b/tst/testinstall/testenumerator.g
similarity index 100%
rename from tst/testenumerator.g
rename to tst/testinstall/testenumerator.g
diff --git a/tst/testrandom.g b/tst/testinstall/testrandom.g
similarity index 100%
rename from tst/testrandom.g
rename to tst/testinstall/testrandom.g