diff --git a/misc/tst-fdset.c b/misc/tst-fdset.c
index 70b7028dad..956e371746 100644
--- a/misc/tst-fdset.c
+++ b/misc/tst-fdset.c
@@ -18,7 +18,7 @@
    <http://www.gnu.org/licenses/>.  */
 
 #include <stdio.h>
-#include <sys/types.h>
+#include <sys/select.h>
 
 static int
 do_test (void)
diff --git a/nptl/pthread_join_common.c b/nptl/pthread_join_common.c
index 5224ee2110..b8b016ccb7 100644
--- a/nptl/pthread_join_common.c
+++ b/nptl/pthread_join_common.c
@@ -20,6 +20,8 @@
 #include <atomic.h>
 #include <stap-probe.h>
 
+#include <sys/time.h>
+
 static void
 cleanup (void *arg)
 {
diff --git a/nptl/tst-cancel4.c b/nptl/tst-cancel4.c
index 60a965d23a..dce93dc03a 100644
--- a/nptl/tst-cancel4.c
+++ b/nptl/tst-cancel4.c
@@ -24,6 +24,7 @@
 #include <stdlib.h>
 #include <string.h>
 #include <sys/types.h>
+#include <sys/select.h>
 #include <sys/socket.h>
 #include <sys/un.h>
 #include <sys/ipc.h>
diff --git a/posix/sys/types.h b/posix/sys/types.h
index 08305cf812..9381695548 100644
--- a/posix/sys/types.h
+++ b/posix/sys/types.h
@@ -93,9 +93,6 @@ __BEGIN_DECLS
 
 /* In BSD <sys/types.h> is expected to define BYTE_ORDER.  */
 # include <endian.h>
-
-/* It also defines `fd_set' and the FD_* macros for `select'.  */
-# include <sys/select.h>
 #endif /* Use misc.  */
 
 __END_DECLS
diff --git a/scripts/check-c++-types.sh b/scripts/check-c++-types.sh
index a8f3cfff7b..141ddf7440 100755
--- a/scripts/check-c++-types.sh
+++ b/scripts/check-c++-types.sh
@@ -46,6 +46,7 @@ while read t; do
 #include <sys/types.h>
 #include <sys/stat.h>
 #include <sys/resource.h>
+#include <sys/select.h>
 #include <unistd.h>
 void foo ($t) { }
 EOF
diff --git a/scripts/check-obsolete-constructs.py b/scripts/check-obsolete-constructs.py
index bd5a97f76b..a051d4e845 100755
--- a/scripts/check-obsolete-constructs.py
+++ b/scripts/check-obsolete-constructs.py
@@ -530,13 +530,13 @@ HEADER_ALLOWED_INCLUDES = {
     # mandated: sys/msg.h -> sys/ipc.h
     #           sys/sem.h -> sys/ipc.h
     #           sys/shm.h -> sys/ipc.h
-    # allowed:  sys/time.h -> sys/select.h
-    #           sys/wait.h -> signal.h
+    #           sys/time.h -> sys/select.h (effectively)
+    # allowed:  sys/wait.h -> signal.h
     "sys/msg.h":                   [ "sys/ipc.h" ],
     "sys/sem.h":                   [ "sys/ipc.h" ],
     "sys/shm.h":                   [ "sys/ipc.h" ],
     "sys/time.h":                  [ "sys/select.h" ],
-    "sys/types.h":                 [ "endian.h", "sys/select.h" ],
+    "sys/types.h":                 [ "endian.h" ],
     "sys/uio.h":                   [ "sys/types.h" ],
     "sys/un.h":                    [ "string.h" ],
     "sys/wait.h":                  [ "signal.h" ],
diff --git a/socket/sys/socket.h b/socket/sys/socket.h
index 1bb90ed67c..ce793dc3e2 100644
--- a/socket/sys/socket.h
+++ b/socket/sys/socket.h
@@ -35,6 +35,10 @@ __BEGIN_DECLS
 # include <bits/types/struct_osockaddr.h>
 #endif
 
+#ifdef __USE_GNU
+struct timespec;
+#endif
+
 /* The following constants should be used for the second parameter of
    `shutdown'.  */
 enum
diff --git a/sunrpc/rpc/svc.h b/sunrpc/rpc/svc.h
index 85d0183d48..c77dcf0c4a 100644
--- a/sunrpc/rpc/svc.h
+++ b/sunrpc/rpc/svc.h
@@ -53,6 +53,7 @@
 
 #include <features.h>
 #include <rpc/rpc_msg.h>
+#include <sys/select.h>
 
 __BEGIN_DECLS
 
diff --git a/sysdeps/nptl/thread_db.h b/sysdeps/nptl/thread_db.h
index d134acaa24..4d949b0c37 100644
--- a/sysdeps/nptl/thread_db.h
+++ b/sysdeps/nptl/thread_db.h
@@ -26,7 +26,7 @@
 #include <stdint.h>
 #include <sys/types.h>
 #include <sys/procfs.h>
-
+#include <bits/types/sigset_t.h>
 
 /* Error codes of the library.  */
 typedef enum
diff --git a/sysdeps/unix/sysv/linux/dl-vdso.h b/sysdeps/unix/sysv/linux/dl-vdso.h
index 9e61ca7423..edecf5faf4 100644
--- a/sysdeps/unix/sysv/linux/dl-vdso.h
+++ b/sysdeps/unix/sysv/linux/dl-vdso.h
@@ -23,6 +23,12 @@
 #include <ldsodefs.h>
 #include <dl-hash.h>
 
+/* This header must declare all functions that might be looked up
+   in the vDSO by code fragments generated by make-syscalls.sh.
+   At present the only such function that isn't covered by the above
+   headers is gettimeofday.  */
+#include <sys/time.h>
+
 /* Create version number record for lookup.  */
 #define PREPARE_VERSION(var, vname, vhash) \
   struct r_found_version var;						      \
diff --git a/sysdeps/unix/sysv/linux/pselect.c b/sysdeps/unix/sysv/linux/pselect.c
index c9406cac09..d1106e9b18 100644
--- a/sysdeps/unix/sysv/linux/pselect.c
+++ b/sysdeps/unix/sysv/linux/pselect.c
@@ -19,7 +19,7 @@
 #include <errno.h>
 #include <signal.h>
 #include <time.h>
-#include <sys/poll.h>
+#include <sys/select.h>
 #include <kernel-features.h>
 #include <sysdep-cancel.h>
 
