diff --git a/t/t7005-editor.sh b/t/t7005-editor.sh
index 2f8404afbb..e83bc8fd89 100755
--- a/t/t7005-editor.sh
+++ b/t/t7005-editor.sh
@@ -7,6 +7,7 @@ test_description='GIT_EDITOR, core.editor, and stuff'
 for i in GIT_EDITOR core_editor EDITOR VISUAL vi
 do
 	cat >e-$i.sh <<-EOF
+	#!$SHELL_PATH
 	echo "Edited by $i" >"\$1"
 	EOF
 	chmod +x e-$i.sh
diff --git a/t/t7502-commit.sh b/t/t7502-commit.sh
index ad42c78d7c..56cd866019 100755
--- a/t/t7502-commit.sh
+++ b/t/t7502-commit.sh
@@ -234,7 +234,7 @@ cat >.git/FAKE_EDITOR <<EOF
 # kill -TERM command added below.
 EOF
 
-test_expect_success 'a SIGTERM should break locks' '
+test_expect_success EXECKEEPSPID 'a SIGTERM should break locks' '
 	echo >>negative &&
 	! "$SHELL_PATH" -c '\''
 	  echo kill -TERM $$ >> .git/FAKE_EDITOR
diff --git a/t/test-lib.sh b/t/test-lib.sh
index 8de5ee1b58..2979e8ea0e 100644
--- a/t/test-lib.sh
+++ b/t/test-lib.sh
@@ -697,10 +697,12 @@ case $(uname -s) in
 	}
 	# no POSIX permissions
 	# backslashes in pathspec are converted to '/'
+	# exec does not inherit the PID
 	;;
 *)
 	test_set_prereq POSIXPERM
 	test_set_prereq BSLASHPSPEC
+	test_set_prereq EXECKEEPSPID
 	;;
 esac