diff --git a/compat.c b/compat.c
index 23e3e5b..7798f7a 100644
--- a/compat.c
+++ b/compat.c
@@ -9,6 +9,7 @@
 #include <dirent.h>
 #include <err.h>
 #include <errno.h>
+#include <fcntl.h>
 #include <limits.h>
 #include <stdlib.h>
 #include <string.h>
@@ -56,9 +57,9 @@ int bst_close_range(unsigned int from, unsigned int to, unsigned int flags)
 	errno = ENOSYS;
 #endif
 
-	if (rc == -1 && errno == ENOSYS) {
-		/* The system call is not implemented. Fall back to the good old
-		   fashioned method.
+	if (rc == -1 && (errno == ENOSYS || errno == EINVAL)) {
+		/* The system call is not implemented, or it doesn't support
+		   CLOSE_RANGE_CLOEXEC. Fall back to the good old fashioned method.
 
 		   Note that this isn't particularly efficient. bst_close_range is
 		   itself called in a loop, which means traversing the list of fds
@@ -88,13 +89,24 @@ int bst_close_range(unsigned int from, unsigned int to, unsigned int flags)
 				continue;
 			}
 
-			/* Note: close takes a signed int, while close_range takes unsigned
-			   ints. I'm not too sure how negative file descriptors are handled
-			   (and I don't care much to be honest) so I'll just hope that the
-			   system call just reads out an unsigned integer kernel-side. */
-
-			if (close((int) fd) == -1) {
-				err(1, "bst_close_range: close %d", fd);
+			/* Note: close/fcntl takes a signed int, while close_range takes
+			   unsigned ints. I'm not too sure how negative file descriptors
+			   are handled (and I don't care much to be honest) so I'll just
+			   hope that the system call just reads out an unsigned integer
+			   kernel-side. */
+
+			if (flags & BST_CLOSE_RANGE_CLOEXEC) {
+				int fdflags = fcntl((int) fd, F_GETFD);
+				if (fdflags == -1) {
+					err(1, "bst_close_range: fcntl %d F_GETFD", fd);
+				}
+				if (fcntl((int) fd, F_SETFD, fdflags | FD_CLOEXEC) == -1) {
+					err(1, "bst_close_range: fcntl %d F_SETFD", fd);
+				}
+			} else {
+				if (close((int) fd) == -1) {
+					err(1, "bst_close_range: close %d", fd);
+				}
 			}
 		}
 
diff --git a/compat.h b/compat.h
index 843e5a1..fbd1159 100644
--- a/compat.h
+++ b/compat.h
@@ -11,6 +11,7 @@
 
 /* From the kernel headers */
 # define BST_CLOSE_RANGE_UNSHARE (1U << 1)
+# define BST_CLOSE_RANGE_CLOEXEC (1U << 2)
 
 size_t strlcpy(char *restrict dst, const char *restrict src, size_t size);
 unsigned int parse_fd(char *optarg);
diff --git a/enter.c b/enter.c
index 1fd643f..b2fbaa3 100644
--- a/enter.c
+++ b/enter.c
@@ -515,6 +515,12 @@ int enter(struct entry_settings *opts)
 		}
 	}
 
+	for (const struct close_range *range = opts->close_fds; range < opts->close_fds + opts->nclose_fds; ++range) {
+		if (bst_close_range(range->from, range->to, BST_CLOSE_RANGE_CLOEXEC) == -1) {
+			err(1, "close_range %d %d", range->from, range->to);
+		}
+	}
+
 	/*
 	 * Only mount a a cgroup hierarchy over sys/fs/cgroup if:
 	 *  1) The user has not specified --no_cgroup_remount
@@ -807,11 +813,6 @@ int enter(struct entry_settings *opts)
 			}
 			const char *init = opts->init + rootlen;
 
-			for (const struct close_range *range = opts->close_fds; range < opts->close_fds + opts->nclose_fds; ++range) {
-				if (bst_close_range(range->from, range->to, BST_CLOSE_RANGE_UNSHARE) == -1) {
-					err(1, "close_range %d %d", range->from, range->to);
-				}
-			}
 			execve(init, argv, opts->envp);
 			err(1, "execve %s", init);
 		}