diff --git a/src/sockmap.c b/src/sockmap.c
index 99e017d..4c60428 100644
--- a/src/sockmap.c
+++ b/src/sockmap.c
@@ -75,6 +75,8 @@ int sockmap(struct clientparam * param, int timeo, int usesplice){
 #endif
  int HASERROR=0;
  int CLIENTTERMREAD = 0, CLIENTTERMWRITE = 0, SERVERTERMREAD = 0, SERVERTERMWRITE = 0;
+ /* the side has hung up: closed by the peer after its own was shut down */
+ int CLIENTHUP = 0, SERVERHUP = 0;
  int after = 0;
  struct pollfd fds[8];
  int fdsc = 0;
@@ -629,6 +631,9 @@ log("done read from server to buf");
 #endif
 						))
 					cli_events |= POLLOUT;
+				/* poll() reports a hang-up whatever is asked, and would
+				   return at once every time: wait for the other side then */
+				if(!cli_events && CLIENTHUP) fds[fdsc].fd = INVALID_SOCKET;
 				if(cli_events){
 					fds[fdsc].fd = param->clisock;
 					fds[fdsc].events = cli_events;
@@ -664,9 +669,13 @@ log("ready to write to client");
 						if(fds[fdsc].events & POLLOUT) CLIENTTERMWRITE = 1;
 					}
 				}
-			} else if(fds[fdsc].revents & (POLLERR|POLLNVAL|POLLHUP)) {
+			} else if(fds[fdsc].revents & (POLLERR|POLLNVAL)) {
 				CLIENTTERMREAD = 1;
 				CLIENTTERMWRITE = 1;
+			} else if(fds[fdsc].revents & POLLHUP) {
+				/* what the client sent before it closed is still to be
+				   read, once the buffer has room for it */
+				CLIENTHUP = 1;
 			}
 			fdsc++;
 
@@ -682,6 +691,7 @@ log("ready to write to client");
 #endif
 						))
 					srv_events |= POLLOUT;
+				if(!srv_events && SERVERHUP) fds[fdsc].fd = INVALID_SOCKET;
 				if(srv_events){
 					fds[fdsc].fd = param->remsock;
 					fds[fdsc].events = srv_events;
@@ -724,9 +734,12 @@ log("server terminated connection");
 						if(fds[fdsc].events & POLLOUT) SERVERTERMWRITE = 1;
 					}
 				}
-			} else if(fds[fdsc].revents & (POLLERR|POLLNVAL|POLLHUP)) {
+			} else if(fds[fdsc].revents & (POLLERR|POLLNVAL)) {
 				SERVERTERMREAD = 1;
 				SERVERTERMWRITE = 1;
+			} else if(fds[fdsc].revents & POLLHUP) {
+				/* the rest of the answer may still be waiting to be read */
+				SERVERHUP = 1;
 			}
 			fdsc++;
 //		}
diff --git a/tests/cases/portmap.py b/tests/cases/portmap.py
index 72be8f7..d456192 100644
--- a/tests/cases/portmap.py
+++ b/tests/cases/portmap.py
@@ -1,5 +1,29 @@
 """The port mappers: tcppm forwards a TCP port, udppm a UDP one."""
 
+import socket
+import threading
+import time
+
+HALFCLOSE_SIZE = 20000000
+
+
+def halfclose_origin(listener):
+    """Answers each connection which asks for something with HALFCLOSE_SIZE
+    bytes, then waits for the client's end of the stream and closes. The
+    connections waiting for the service to start ask nothing."""
+    while True:
+        try:
+            c, _ = listener.accept()
+        except OSError:
+            return
+        try:
+            if c.recv(1000):
+                c.sendall(b"x" * HALFCLOSE_SIZE)
+                c.recv(10)
+        except OSError:
+            pass
+        c.close()
+
 
 def run(t):
     # --- tcppm ---------------------------------------------------------
@@ -40,6 +64,41 @@ def run(t):
 
     t.stop_all()
 
+    # A client which shuts down its sending side still gets the whole answer,
+    # even when it reads slowly: the server has finished and closed by then,
+    # and the rest of the answer waits in the proxy's buffer and the kernel's.
+    listener = socket.socket()
+    listener.bind(("127.0.0.1", 0))
+    listener.listen(1)
+    threading.Thread(target=halfclose_origin, args=(listener,), daemon=True).start()
+    halfclosed = t.free_port()
+    t.start("portmap_halfclose", f"""
+        log
+        auth none
+        tcppm {halfclosed} 127.0.0.1 {listener.getsockname()[1]}
+    """, ports=[halfclosed])
+    s = socket.socket()
+    s.setsockopt(socket.SOL_SOCKET, socket.SO_RCVBUF, 32768)
+    s.settimeout(30)
+    got = 0
+    try:
+        s.connect(("127.0.0.1", halfclosed))
+        s.sendall(b"request")
+        s.shutdown(socket.SHUT_WR)
+        time.sleep(1)
+        while True:
+            d = s.recv(65536)
+            if not d:
+                break
+            got += len(d)
+    except OSError:
+        pass
+    s.close()
+    listener.close()
+    t.eq(HALFCLOSE_SIZE, got, "a half-closed client reading slowly gets the whole answer")
+
+    t.stop_all()
+
     # --- udppm ---------------------------------------------------------
     # something has to be listening for the mapped datagrams to go anywhere
     echo = t.udp_echo()