diff --git a/t/Makefile b/t/Makefile
index aa952e1c5c..ed49c20b16 100644
--- a/t/Makefile
+++ b/t/Makefile
@@ -39,4 +39,3 @@ full-svn-test:
 	$(MAKE) $(TSVN) GIT_SVN_NO_OPTIMIZE_COMMITS=0 LC_ALL=en_US.UTF-8
 
 .PHONY: pre-clean $(T) aggregate-results clean
-.NOTPARALLEL:
diff --git a/t/test-lib.sh b/t/test-lib.sh
index 11c027571b..7f60b614ea 100644
--- a/t/test-lib.sh
+++ b/t/test-lib.sh
@@ -449,6 +449,11 @@ test_done () {
 		# we will leave things as they are.
 
 		say_color pass "passed all $msg"
+
+		test -d "$remove_trash" &&
+		cd "$(dirname "$remove_trash")" &&
+		rm -rf "$(basename "$remove_trash")"
+
 		exit 0 ;;
 
 	*)
@@ -485,7 +490,8 @@ fi
 . ../GIT-BUILD-OPTIONS
 
 # Test repository
-test="trash directory"
+test="trash directory.$(basename "$0" .sh)"
+remove_trash="$TEST_DIRECTORY/$test"
 rm -fr "$test" || {
 	trap - exit
 	echo >&5 "FATAL: Cannot prepare test area"