diff --git a/CMakeLists.txt b/CMakeLists.txt
index 223d777989c..aeba3dd309f 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -303,6 +303,7 @@ set(BASIC_TESTS
   fault_in_code_page
   fcntl_owner_ex
   fcntl_dupfd
+  fds_clean
   flock
   flock2
   fork_child_crash
diff --git a/include/rr/rr.h b/include/rr/rr.h
index 1e0eb45968c..f853bf15eeb 100644
--- a/include/rr/rr.h
+++ b/include/rr/rr.h
@@ -28,4 +28,13 @@
  */
 #define RR_RESERVED_ROOT_DIR_FD 1000
 
+/**
+ * The preferred fd that rr uses to control tracee desched. Some software
+ * (e.g. the chromium IPC code) wants to have the first few fds all to itself,
+ * so we need to stay above some floor. Tracee close()es of the fd that is
+ * actually assigned will be silently ignored, and tracee dup()s to that fd will
+ * fail with EBADF.
+ */
+#define RR_DESCHED_EVENT_FLOOR_FD 100
+
 #endif /* RR_H_ */
diff --git a/src/preload/preload.c b/src/preload/preload.c
index 0a05d16a1ce..446cf972841 100644
--- a/src/preload/preload.c
+++ b/src/preload/preload.c
@@ -55,6 +55,7 @@
 #include <linux/perf_event.h>
 #include <poll.h>
 #include <pthread.h>
+#include "rr/rr.h"
 #include <signal.h>
 #include <stdarg.h>
 #include <stdlib.h>
@@ -74,10 +75,6 @@
 #include <time.h>
 #include <unistd.h>
 
-#ifndef PERF_FLAG_FD_CLOEXEC
-#define PERF_FLAG_FD_CLOEXEC (1 << 3)
-#endif
-
 /* NB: don't include any other local headers here. */
 
 #ifdef memcpy
@@ -322,6 +319,10 @@ static long traced_raw_syscall(const struct syscall_info* call) {
 #define RR_FCNTL_SYSCALL SYS_fcntl
 #endif
 
+static int privileged_traced_close(int fd) {
+  return privileged_traced_syscall1(SYS_close, fd);
+}
+
 static int privileged_traced_fcntl(int fd, int cmd, ...) {
   va_list ap;
   void* arg;
@@ -518,7 +519,7 @@ static void rrcall_init_buffers(struct rrcall_init_buffers_params* args) {
  */
 static int open_desched_event_counter(size_t nr_descheds, pid_t tid) {
   struct perf_event_attr attr;
-  int fd;
+  int tmp_fd, fd;
   struct f_owner_ex own;
 
   memset(&attr, 0, sizeof(attr));
@@ -528,15 +529,17 @@ static int open_desched_event_counter(size_t nr_descheds, pid_t tid) {
   attr.disabled = 1;
   attr.sample_period = nr_descheds;
 
-  fd = privileged_traced_perf_event_open(&attr, 0 /*self*/, -1 /*any cpu*/, -1,
-                                         PERF_FLAG_FD_CLOEXEC);
-  if (0 > fd && errno == EINVAL) {
-    /* Maybe PERF_FLAG_FD_CLOEXEC is not understood by this kernel. */
-    fd = privileged_traced_perf_event_open(&attr, 0 /*self*/, -1 /*any cpu*/,
-                                           -1, 0);
+  tmp_fd = privileged_traced_perf_event_open(&attr, 0 /*self*/, -1 /*any cpu*/,
+                                             -1, 0);
+  if (0 > tmp_fd) {
+    fatal("Failed to perf_event_open(cs, period=%zu)", nr_descheds);
   }
+  fd = privileged_traced_fcntl(tmp_fd, F_DUPFD_CLOEXEC, RR_DESCHED_EVENT_FLOOR_FD);
   if (0 > fd) {
-    fatal("Failed to perf_event_open(cs, period=%zu)", nr_descheds);
+    fatal("Failed to dup desched fd");
+  }
+  if (privileged_traced_close(tmp_fd)) {
+    fatal("Failed to close tmp_fd");
   }
   if (privileged_traced_fcntl(fd, F_SETFL, O_ASYNC)) {
     fatal("Failed to fcntl(O_ASYNC) the desched counter");
diff --git a/src/test/fds_clean.c b/src/test/fds_clean.c
new file mode 100644
index 00000000000..3b0342fe2eb
--- /dev/null
+++ b/src/test/fds_clean.c
@@ -0,0 +1,15 @@
+/* -*- Mode: C; tab-width: 8; c-basic-offset: 2; indent-tabs-mode: nil; -*- */
+
+#include "rrutil.h"
+
+int main(int argc, char** argv) {
+  int fd;
+
+  for (fd = 3; fd < 100; ++fd) {
+    /* Check that |fd| is available to us. */
+    test_assert(dup2(2, fd) == fd);
+  }
+
+  atomic_puts("EXIT-SUCCESS");
+  return 0;
+}