diff --git a/t/t5505-remote.sh b/t/t5505-remote.sh
index c90cf47acd..af4e0a1e72 100755
--- a/t/t5505-remote.sh
+++ b/t/t5505-remote.sh
@@ -923,11 +923,12 @@ test_expect_success 'migrate a remote from named file in $GIT_DIR/remotes' '
 '
 
 test_expect_success 'migrate a remote from named file in $GIT_DIR/branches' '
-	git clone one six &&
+	git clone --template= one six &&
 	origin_url=$(pwd)/one &&
 	(
 		cd six &&
 		git remote rm origin &&
+		mkdir .git/branches &&
 		echo "$origin_url#main" >.git/branches/origin &&
 		git remote rename origin origin &&
 		test_path_is_missing .git/branches/origin &&
@@ -938,10 +939,11 @@ test_expect_success 'migrate a remote from named file in $GIT_DIR/branches' '
 '
 
 test_expect_success 'migrate a remote from named file in $GIT_DIR/branches (2)' '
-	git clone one seven &&
+	git clone --template= one seven &&
 	(
 		cd seven &&
 		git remote rm origin &&
+		mkdir .git/branches &&
 		echo "quux#foom" > .git/branches/origin &&
 		git remote rename origin origin &&
 		test_path_is_missing .git/branches/origin &&
diff --git a/t/t5516-fetch-push.sh b/t/t5516-fetch-push.sh
index 4dfb080433..5d3054eeb8 100755
--- a/t/t5516-fetch-push.sh
+++ b/t/t5516-fetch-push.sh
@@ -17,6 +17,7 @@ This test checks the following functionality:
 GIT_TEST_DEFAULT_INITIAL_BRANCH_NAME=main
 export GIT_TEST_DEFAULT_INITIAL_BRANCH_NAME
 
+TEST_CREATE_REPO_NO_TEMPLATE=1
 . ./test-lib.sh
 
 D=$(pwd)
@@ -25,7 +26,8 @@ mk_empty () {
 	repo_name="$1"
 	test_when_finished "rm -rf \"$repo_name\"" &&
 	test_path_is_missing "$repo_name" &&
-	git init "$repo_name" &&
+	git init --template= "$repo_name" &&
+	mkdir "$repo_name"/.git/hooks &&
 	git -C "$repo_name" config receive.denyCurrentBranch warn
 }
 
@@ -77,7 +79,7 @@ mk_test_with_hooks() {
 
 mk_child() {
 	test_when_finished "rm -rf \"$2\"" &&
-	git clone "$1" "$2"
+	git clone --template= "$1" "$2"
 }
 
 check_push_result () {
@@ -916,6 +918,7 @@ test_expect_success 'fetch with branches' '
 	mk_empty testrepo &&
 	git branch second $the_first_commit &&
 	git checkout second &&
+	mkdir testrepo/.git/branches &&
 	echo ".." > testrepo/.git/branches/branch1 &&
 	(
 		cd testrepo &&
@@ -929,6 +932,7 @@ test_expect_success 'fetch with branches' '
 
 test_expect_success 'fetch with branches containing #' '
 	mk_empty testrepo &&
+	mkdir testrepo/.git/branches &&
 	echo "..#second" > testrepo/.git/branches/branch2 &&
 	(
 		cd testrepo &&
@@ -943,7 +947,11 @@ test_expect_success 'fetch with branches containing #' '
 test_expect_success 'push with branches' '
 	mk_empty testrepo &&
 	git checkout second &&
+
+	test_when_finished "rm -rf .git/branches" &&
+	mkdir .git/branches &&
 	echo "testrepo" > .git/branches/branch1 &&
+
 	git push branch1 &&
 	(
 		cd testrepo &&
@@ -955,7 +963,11 @@ test_expect_success 'push with branches' '
 
 test_expect_success 'push with branches containing #' '
 	mk_empty testrepo &&
+
+	test_when_finished "rm -rf .git/branches" &&
+	mkdir .git/branches &&
 	echo "testrepo#branch3" > .git/branches/branch2 &&
+
 	git push branch2 &&
 	(
 		cd testrepo &&
diff --git a/t/test-lib.sh b/t/test-lib.sh
index 531cef097d..eb6d14fea7 100644
--- a/t/test-lib.sh
+++ b/t/test-lib.sh
@@ -1528,7 +1528,9 @@ remove_trash_directory "$TRASH_DIRECTORY" || {
 remove_trash=t
 if test -z "$TEST_NO_CREATE_REPO"
 then
-	git init "$TRASH_DIRECTORY" >&3 2>&4 ||
+	git init \
+	    ${TEST_CREATE_REPO_NO_TEMPLATE:+--template=} \
+	    "$TRASH_DIRECTORY" >&3 2>&4 ||
 	error "cannot run git init"
 else
 	mkdir -p "$TRASH_DIRECTORY"