diff --git a/ci/run-build-and-tests.sh b/ci/run-build-and-tests.sh
index 7a1466b868..2528f25e31 100755
--- a/ci/run-build-and-tests.sh
+++ b/ci/run-build-and-tests.sh
@@ -50,8 +50,6 @@ if test -n "$run_tests"
 then
 	group "Run tests" make test ||
 	handle_failed_tests
-	group "Run unit tests" \
-		make DEFAULT_UNIT_TEST_TARGET=unit-tests-prove unit-tests
 fi
 check_unignored_build_artifacts
 
diff --git a/t/Makefile b/t/Makefile
index 0ae04f1e42..b2eb9f770b 100644
--- a/t/Makefile
+++ b/t/Makefile
@@ -68,7 +68,7 @@ failed:
 	test -z "$$failed" || $(MAKE) $$failed
 
 prove: pre-clean check-chainlint $(TEST_LINT)
-	@echo "*** prove ***"; $(CHAINLINTSUPPRESS) $(PROVE) --exec '$(TEST_SHELL_PATH_SQ)' $(GIT_PROVE_OPTS) $(T) :: $(GIT_TEST_OPTS)
+	@echo "*** prove (shell & unit tests) ***"; $(CHAINLINTSUPPRESS) TEST_SHELL_PATH='$(TEST_SHELL_PATH_SQ)' $(PROVE) --exec ./run-test.sh $(GIT_PROVE_OPTS) $(T) $(UNIT_TESTS) :: $(GIT_TEST_OPTS)
 	$(MAKE) clean-except-prove-cache
 
 $(T):
diff --git a/t/run-test.sh b/t/run-test.sh
new file mode 100755
index 0000000000..13c353b91b
--- /dev/null
+++ b/t/run-test.sh
@@ -0,0 +1,18 @@
+#!/bin/sh
+
+# A simple wrapper to run shell tests via TEST_SHELL_PATH,
+# or exec unit tests directly.
+
+case "$1" in
+*.sh)
+	if test -z "${TEST_SHELL_PATH}"
+	then
+		echo >&2 "ERROR: TEST_SHELL_PATH is empty or not set"
+		exit 1
+	fi
+	exec "${TEST_SHELL_PATH}" "$@"
+	;;
+*)
+	exec "$@"
+	;;
+esac