--- a/tst/testall.g
+++ b/tst/testall.g
@@ -1,5 +1,51 @@
 LoadPackage( "hap" );
 
+exclude:=[];
+
+if PositionSublist(GAPInfo.SystemEnvironment.DEB_BUILD_OPTIONS,
+                   "fullcheck") = fail then
+  Append(exclude, ["1.6.1.tst", "1.6.4.tst",
+                   "1.7.3.tst",
+                   "1.99.1.tst", "1.99.6.tst",
+                   "2.4.8.tst", "2.7.4.tst",
+                   "3.10.2.tst", "3.10.3.tst",
+                   "3.7.5.tst",
+                   "4.1.1.tst", "4.1.2.tst"]);
+fi;
+
+# HAPprime
+if LoadPackage( "singular" ) <> true then
+  Append(exclude, ["3.9.1.tst", "3.9.3.tst"]);
+fi;
+
+# TransGrp
+if LoadPackage( "TransGrp" ) <> true then
+  Append(exclude, ["0hap.tst","1.5.3.tst"]);
+fi;
+
+# Congruence
+if LoadPackage( "Congruence" ) <> true then
+  Append(exclude, ["3.3.5.tst","3.7.1.tst"]);
+fi;
+
+# HAPCryst
+if LoadPackage( "HAPCryst" ) <> true then
+  Append(exclude, ["1.8.2.tst","1.9.1.tst",
+                   "2.5.1.tst","3.1.2.tst",
+                   "3.1.3.tst","3.1.4.tst",
+                   "3.3.3.tst","3.3.6.tst"]);
+fi;
+
+# Polymaking
+if LoadPackage( "Polymaking" ) <> true then
+  Append(exclude, ["1.1.1.tst","1.2.1.tst",
+                   "1.8.2.tst","1.9.1.tst",
+                   "2.2.1.tst","2.5.1.tst",
+                   "3.1.2.tst","3.1.3.tst",
+                   "3.1.4.tst","3.2.1.tst",
+                   "3.3.3.tst","3.3.6.tst"]);
+fi;
+
 if not GAPInfo.Architecture="x86_64-pc-linux-gnu-default32-kv8" then
 
 TestDirectory(
@@ -8,7 +54,8 @@
 DirectoriesPackageLibrary( "hap", "tst/testextra" ),
 DirectoriesPackageLibrary( "hap", "tst/testextra2" ),
 DirectoriesPackageLibrary( "hap", "tst/testall3" )],
-rec(exitGAP     := true,
+rec(exclude     := exclude,
+    exitGAP     := true,
     testOptions := rec(compareFunction := "uptowhitespace") ) );
 
 else
@@ -19,7 +66,8 @@
 DirectoriesPackageLibrary( "hap", "tst/testextra" ),
 DirectoriesPackageLibrary( "hap", "tst/testextra2" )],
 #DirectoriesPackageLibrary( "hap", "tst/testall3" )],
-rec(exitGAP     := true,
+rec(exclude     := exclude,
+    exitGAP     := true,
     testOptions := rec(compareFunction := "uptowhitespace") ) );
 fi;
 
