diff --git a/linux_dep.h b/linux_dep.h
index 3a41e42..240f50a 100644
--- a/linux_dep.h
+++ b/linux_dep.h
@@ -127,22 +127,18 @@ struct tcp_info_linux {
 
 #include <linux/close_range.h>
 
-#ifdef CLOSE_RANGE_UNSHARE	/* Linux kernel >= 5.9 */
 /* glibc < 2.34 and musl as of 1.2.5 need these */
 #ifndef SYS_close_range
 #define SYS_close_range		436
 #endif
+#ifndef CLOSE_RANGE_UNSHARE	/* Linux kernel < 5.9 */
+#define CLOSE_RANGE_UNSHARE	(1U << 1)
+#endif
+
 __attribute__ ((weak))
 /* cppcheck-suppress funcArgNamesDifferent */
 int close_range(unsigned int first, unsigned int last, int flags) {
 	return syscall(SYS_close_range, first, last, flags);
 }
-#else
-/* No reasonable fallback option */
-/* cppcheck-suppress funcArgNamesDifferent */
-int close_range(unsigned int first, unsigned int last, int flags) {
-	return 0;
-}
-#endif
 
 #endif /* LINUX_DEP_H */
diff --git a/util.c b/util.c
index 913f34b..126dedb 100644
--- a/util.c
+++ b/util.c
@@ -738,8 +738,20 @@ void close_open_files(int argc, char **argv)
 			rc = close_range(fd + 1, ~0U, CLOSE_RANGE_UNSHARE);
 	}
 
-	if (rc)
-		die_perror("Failed to close files leaked by parent");
+	if (rc) {
+		if (errno == ENOSYS || errno == EINVAL) {
+			/* This probably means close_range() or the
+			 * CLOSE_RANGE_UNSHARE flag is not supported by the
+			 * kernel.  Not much we can do here except carry on and
+			 * hope for the best.
+			 */
+			warn(
+"Can't use close_range() to ensure no files leaked by parent");
+		} else {
+			die_perror("Failed to close files leaked by parent");
+		}
+	}
+
 }
 
 /**