diff --git a/src/gnutls.c b/src/gnutls.c
index 903393fed1..e7d0d3d845 100644
--- a/src/gnutls.c
+++ b/src/gnutls.c
@@ -708,16 +708,18 @@ emacs_gnutls_read (struct Lisp_Process *proc, char *buf, ptrdiff_t nbyte)
   rtnval = gnutls_record_recv (state, buf, nbyte);
   if (rtnval >= 0)
     return rtnval;
-  else if (rtnval == GNUTLS_E_UNEXPECTED_PACKET_LENGTH)
-    /* The peer closed the connection. */
-    return 0;
   else if (emacs_gnutls_handle_error (state, rtnval))
-    /* non-fatal error */
-    return -1;
-  else {
-    /* a fatal error occurred */
-    return 0;
-  }
+    {
+      /* non-fatal error */
+      errno = EAGAIN;
+      return -1;
+    }
+  else
+    {
+      /* a fatal error occurred */
+      errno = EPROTO;
+      return 0;
+    }
 }
 
 static char const *
@@ -756,8 +758,10 @@ emacs_gnutls_handle_error (gnutls_session_t session, int err)
 	 connection.  */
 # ifdef HAVE_GNUTLS3
       if (err == GNUTLS_E_PREMATURE_TERMINATION)
-	level = 3;
+# else
+      if (err == GNUTLS_E_UNEXPECTED_PACKET_LENGTH)
 # endif
+	level = 3;
 
       GNUTLS_LOG2 (level, max_log_level, "fatal error:", str);
       ret = false;
diff --git a/src/process.c b/src/process.c
index 9b9b9f3550..f8fed56d5b 100644
--- a/src/process.c
+++ b/src/process.c
@@ -5392,60 +5392,31 @@ wait_reading_process_output (intmax_t time_limit, int nsecs, int read_kbd,
 #endif	/* !HAVE_GLIB */
 
 #ifdef HAVE_GNUTLS
-          /* GnuTLS buffers data internally.  In lowat mode it leaves
-             some data in the TCP buffers so that select works, but
-             with custom pull/push functions we need to check if some
-             data is available in the buffers manually.  */
-          if (nfds == 0)
+          /* GnuTLS buffers data internally. select() will only report
+             available data for the underlying kernel sockets API, not
+             what has been buffered internally. As such, we need to loop
+             through all channels and check for available data manually.  */
+          if (nfds >= 0)
 	    {
-	      fd_set tls_available;
-	      int set = 0;
-
-	      FD_ZERO (&tls_available);
-	      if (! wait_proc)
-		{
-		  /* We're not waiting on a specific process, so loop
-		     through all the channels and check for data.
-		     This is a workaround needed for some versions of
-		     the gnutls library -- 2.12.14 has been confirmed
-		     to need it.  See
-		     http://comments.gmane.org/gmane.emacs.devel/145074 */
-		  for (channel = 0; channel < FD_SETSIZE; ++channel)
-		    if (! NILP (chan_process[channel]))
-		      {
-			struct Lisp_Process *p =
-			  XPROCESS (chan_process[channel]);
-			if (p && p->gnutls_p && p->gnutls_state
-			    && ((emacs_gnutls_record_check_pending
-				 (p->gnutls_state))
-				> 0))
-			  {
-			    nfds++;
-			    eassert (p->infd == channel);
-			    FD_SET (p->infd, &tls_available);
-			    set++;
-			  }
-		      }
-		}
-	      else
-		{
-		  /* Check this specific channel.  */
-		  if (wait_proc->gnutls_p /* Check for valid process.  */
-		      && wait_proc->gnutls_state
-		      /* Do we have pending data?  */
-		      && ((emacs_gnutls_record_check_pending
-			   (wait_proc->gnutls_state))
-			  > 0))
-		    {
-		      nfds = 1;
-		      eassert (0 <= wait_proc->infd);
-		      /* Set to Available.  */
-		      FD_SET (wait_proc->infd, &tls_available);
-		      set++;
-		    }
-		}
-	      if (set)
-		Available = tls_available;
+              for (channel = 0; channel < FD_SETSIZE; ++channel)
+                if (! NILP (chan_process[channel]))
+                  {
+                    struct Lisp_Process *p =
+                      XPROCESS (chan_process[channel]);
+
+                    if (just_wait_proc && p != wait_proc)
+                      continue;
+
+                    if (p && p->gnutls_p && p->gnutls_state
+                        && ((emacs_gnutls_record_check_pending
+                             (p->gnutls_state))
+                            > 0))
+                      {
+                        nfds++;
+                        eassert (p->infd == channel);
+                        FD_SET (p->infd, &Available);
+                      }
+                  }
 	    }
 #endif
 	}
diff --git a/src/xgselect.c b/src/xgselect.c
index fedd3127ef..f68982143e 100644
--- a/src/xgselect.c
+++ b/src/xgselect.c
@@ -143,6 +143,14 @@ xg_select (int fds_lim, fd_set *rfds, fd_set *wfds, fd_set *efds,
             ++retval;
         }
     }
+  else if (nfds == 0)
+    {
+      // pselect() clears the file descriptor sets if no fd is ready (but
+      // not if an error occurred), so should we to be compatible. (Bug#21337)
+      if (rfds) FD_ZERO (rfds);
+      if (wfds) FD_ZERO (wfds);
+      if (efds) FD_ZERO (efds);
+    }
 
   /* If Gtk+ is in use eventually gtk_main_iteration will be called,
      unless retval is zero.  */