diff --git a/t/t4014-format-patch.sh b/t/t4014-format-patch.sh
index 8049cad374..805dc9012d 100755
--- a/t/t4014-format-patch.sh
+++ b/t/t4014-format-patch.sh
@@ -1072,7 +1072,7 @@ test_expect_success '--from omits redundant in-body header' '
 '
 
 test_expect_success 'in-body headers trigger content encoding' '
-	GIT_AUTHOR_NAME="éxötìc" test_commit exotic &&
+	test_env GIT_AUTHOR_NAME="éxötìc" test_commit exotic &&
 	test_when_finished "git reset --hard HEAD^" &&
 	git format-patch -1 --stdout --from >patch &&
 	cat >expect <<-\EOF &&
diff --git a/t/t5500-fetch-pack.sh b/t/t5500-fetch-pack.sh
index 91a69fc33a..82d913a6a8 100755
--- a/t/t5500-fetch-pack.sh
+++ b/t/t5500-fetch-pack.sh
@@ -558,7 +558,6 @@ check_prot_path () {
 }
 
 check_prot_host_port_path () {
-	local diagport
 	case "$2" in
 		*ssh*)
 		pp=ssh
diff --git a/t/t7403-submodule-sync.sh b/t/t7403-submodule-sync.sh
index 79bc135bf6..5503ec067f 100755
--- a/t/t7403-submodule-sync.sh
+++ b/t/t7403-submodule-sync.sh
@@ -62,13 +62,13 @@ test_expect_success 'change submodule' '
 '
 
 reset_submodule_urls () {
-	local root
-	root=$(pwd) &&
 	(
+		root=$(pwd) &&
 		cd super-clone/submodule &&
 		git config remote.origin.url "$root/submodule"
 	) &&
 	(
+		root=$(pwd) &&
 		cd super-clone/submodule/sub-submodule &&
 		git config remote.origin.url "$root/submodule"
 	)
diff --git a/t/test-lib-functions.sh b/t/test-lib-functions.sh
index 3978fc0b45..48884d5208 100644
--- a/t/test-lib-functions.sh
+++ b/t/test-lib-functions.sh
@@ -939,3 +939,25 @@ mingw_read_file_strip_cr_ () {
 		eval "$1=\$$1\$line"
 	done
 }
+
+# Like "env FOO=BAR some-program", but run inside a subshell, which means
+# it also works for shell functions (though those functions cannot impact
+# the environment outside of the test_env invocation).
+test_env () {
+	(
+		while test $# -gt 0
+		do
+			case "$1" in
+			*=*)
+				eval "${1%%=*}=\${1#*=}"
+				eval "export ${1%%=*}"
+				shift
+				;;
+			*)
+				"$@"
+				exit
+				;;
+			esac
+		done
+	)
+}