diff --git a/docs/ENVIRONMENT.md b/docs/ENVIRONMENT.md
index 791ba8dd12..2ba222d3a6 100644
--- a/docs/ENVIRONMENT.md
+++ b/docs/ENVIRONMENT.md
@@ -341,7 +341,7 @@ the journal instead of only when logging in debug mode.
 
 `systemd-sysusers`
 
-* `SOURCE_DATE_EPOCH` — if unset, the field of the date of last password change
+* `$SOURCE_DATE_EPOCH` — if unset, the field of the date of last password change
   in `/etc/shadow` will be the number of days from Jan 1, 1970 00:00 UTC until
   today. If `$SOURCE_DATE_EPOCH` is set to a valid UNIX epoch value in seconds,
   then the field will be the number of days until that time instead. This is to
diff --git a/src/test/test-async.c b/src/test/test-async.c
index b97fedcfc6..69785e47fa 100644
--- a/src/test/test-async.c
+++ b/src/test/test-async.c
@@ -4,8 +4,9 @@
 #include <unistd.h>
 
 #include "async.h"
-#include "macro.h"
+#include "fs-util.h"
 #include "tmpfile-util.h"
+#include "tests.h"
 
 static bool test_async = false;
 
@@ -15,24 +16,22 @@ static void *async_func(void *arg) {
         return NULL;
 }
 
-int main(int argc, char *argv[]) {
+TEST(test_async) {
+        _cleanup_(unlink_tempfilep) char name[] = "/tmp/test-asynchronous_close.XXXXXX";
         int fd;
-        char name[] = "/tmp/test-asynchronous_close.XXXXXX";
 
         fd = mkostemp_safe(name);
         assert_se(fd >= 0);
         asynchronous_close(fd);
 
         assert_se(asynchronous_job(async_func, NULL) >= 0);
-
         assert_se(asynchronous_sync(NULL) >= 0);
 
         sleep(1);
 
         assert_se(fcntl(fd, F_GETFD) == -1);
+        assert_se(errno == EBADF);
         assert_se(test_async);
-
-        (void) unlink(name);
-
-        return 0;
 }
+
+DEFINE_TEST_MAIN(LOG_DEBUG);