diff --git a/sha1_file.c b/sha1_file.c
index ee224e4128..a2ff2961b1 100644
--- a/sha1_file.c
+++ b/sha1_file.c
@@ -807,15 +807,38 @@ void free_pack_by_name(const char *pack_name)
 static unsigned int get_max_fd_limit(void)
 {
 #ifdef RLIMIT_NOFILE
-	struct rlimit lim;
+	{
+		struct rlimit lim;
 
-	if (getrlimit(RLIMIT_NOFILE, &lim))
-		die_errno("cannot get RLIMIT_NOFILE");
+		if (!getrlimit(RLIMIT_NOFILE, &lim))
+			return lim.rlim_cur;
+	}
+#endif
 
-	return lim.rlim_cur;
-#elif defined(_SC_OPEN_MAX)
-	return sysconf(_SC_OPEN_MAX);
-#elif defined(OPEN_MAX)
+#ifdef _SC_OPEN_MAX
+	{
+		long open_max = sysconf(_SC_OPEN_MAX);
+		if (0 < open_max)
+			return open_max;
+		/*
+		 * Otherwise, we got -1 for one of the two
+		 * reasons:
+		 *
+		 * (1) sysconf() did not understand _SC_OPEN_MAX
+		 *     and signaled an error with -1; or
+		 * (2) sysconf() said there is no limit.
+		 *
+		 * We _could_ clear errno before calling sysconf() to
+		 * tell these two cases apart and return a huge number
+		 * in the latter case to let the caller cap it to a
+		 * value that is not so selfish, but letting the
+		 * fallback OPEN_MAX codepath take care of these cases
+		 * is a lot simpler.
+		 */
+	}
+#endif
+
+#ifdef OPEN_MAX
 	return OPEN_MAX;
 #else
 	return 1; /* see the caller ;-) */