diff --git a/agentf.c b/agentf.c
index 69ede15e..3fab01a9 100644
--- a/agentf.c
+++ b/agentf.c
@@ -155,7 +155,7 @@ static const struct ChannelVtable agentf_channelvt = {
     agentf_send_eof,
     agentf_set_input_wanted,
     agentf_log_close_msg,
-    chan_no_eager_close,
+    chan_default_want_close,
     chan_no_exit_status,
     chan_no_exit_signal,
     chan_no_exit_signal_numeric,
diff --git a/mainchan.c b/mainchan.c
index 524a0fc8..1ee731a6 100644
--- a/mainchan.c
+++ b/mainchan.c
@@ -33,7 +33,7 @@ static const struct ChannelVtable mainchan_channelvt = {
     mainchan_send_eof,
     mainchan_set_input_wanted,
     mainchan_log_close_msg,
-    chan_no_eager_close,
+    chan_default_want_close,
     mainchan_rcvd_exit_status,
     mainchan_rcvd_exit_signal,
     mainchan_rcvd_exit_signal_numeric,
diff --git a/portfwd.c b/portfwd.c
index dbba3889..6d8d1153 100644
--- a/portfwd.c
+++ b/portfwd.c
@@ -450,7 +450,7 @@ static const struct ChannelVtable PortForwarding_channelvt = {
     pfd_send_eof,
     pfd_set_input_wanted,
     pfd_log_close_msg,
-    chan_no_eager_close,
+    chan_default_want_close,
     chan_no_exit_status,
     chan_no_exit_signal,
     chan_no_exit_signal_numeric,
diff --git a/ssh2connection.c b/ssh2connection.c
index 52b8e0f8..e6e2fd14 100644
--- a/ssh2connection.c
+++ b/ssh2connection.c
@@ -1153,9 +1153,8 @@ static void ssh2_channel_check_close(struct ssh2_channel *c)
         return;
     }
 
-    if ((!((CLOSES_SENT_EOF | CLOSES_RCVD_EOF) & ~c->closes) ||
-         chan_want_close(c->chan, (c->closes & CLOSES_SENT_EOF),
-                         (c->closes & CLOSES_RCVD_EOF))) &&
+    if (chan_want_close(c->chan, (c->closes & CLOSES_SENT_EOF),
+                        (c->closes & CLOSES_RCVD_EOF)) &&
 	!c->chanreq_head &&
 	!(c->closes & CLOSES_SENT_CLOSE)) {
         /*
diff --git a/sshchan.h b/sshchan.h
index 3b221481..63f13136 100644
--- a/sshchan.h
+++ b/sshchan.h
@@ -75,7 +75,7 @@ void chan_remotely_opened_failure(Channel *chan, const char *errtext);
 
 /* want_close for any channel that wants the default behaviour of not
  * closing until both directions have had an EOF */
-int chan_no_eager_close(Channel *, int, int);
+int chan_default_want_close(Channel *, int, int);
 
 /* default implementations that refuse all the channel requests */
 int chan_no_exit_status(Channel *, int);
diff --git a/sshcommon.c b/sshcommon.c
index ec206c60..48eeff1b 100644
--- a/sshcommon.c
+++ b/sshcommon.c
@@ -339,9 +339,14 @@ void chan_remotely_opened_failure(Channel *chan, const char *errtext)
     assert(0 && "this channel type should never receive OPEN_FAILURE");
 }
 
-int chan_no_eager_close(Channel *chan, int sent_local_eof, int rcvd_remote_eof)
+int chan_default_want_close(
+    Channel *chan, int sent_local_eof, int rcvd_remote_eof)
 {
-    return FALSE;     /* default: never proactively ask for a close */
+    /*
+     * Default close policy: we start initiating the CHANNEL_CLOSE
+     * procedure as soon as both sides of the channel have seen EOF.
+     */
+    return sent_local_eof && rcvd_remote_eof;
 }
 
 int chan_no_exit_status(Channel *chan, int status)
diff --git a/unix/uxpgnt.c b/unix/uxpgnt.c
index 55e7981a..a0c48ca3 100644
--- a/unix/uxpgnt.c
+++ b/unix/uxpgnt.c
@@ -124,7 +124,7 @@ static int time_to_die = FALSE;
  * forwarding too. */
 void chan_remotely_opened_confirmation(Channel *chan) { }
 void chan_remotely_opened_failure(Channel *chan, const char *err) { }
-int chan_no_eager_close(Channel *chan, int s, int r) { return FALSE; }
+int chan_default_want_close(Channel *chan, int s, int r) { return FALSE; }
 int chan_no_exit_status(Channel *ch, int s) { return FALSE; }
 int chan_no_exit_signal(Channel *ch, ptrlen s, int c, ptrlen m)
 { return FALSE; }
diff --git a/x11fwd.c b/x11fwd.c
index 44c9df1e..8e306f42 100644
--- a/x11fwd.c
+++ b/x11fwd.c
@@ -730,7 +730,7 @@ static const struct ChannelVtable X11Connection_channelvt = {
     x11_send_eof,
     x11_set_input_wanted,
     x11_log_close_msg,
-    chan_no_eager_close,
+    chan_default_want_close,
     chan_no_exit_status,
     chan_no_exit_signal,
     chan_no_exit_signal_numeric,