diff --git a/lib/multi.c b/lib/multi.c
index 685bb01f0c..e72d3e3d4a 100644
--- a/lib/multi.c
+++ b/lib/multi.c
@@ -294,7 +294,8 @@ struct Curl_multi *Curl_multi_handle(uint32_t xfer_table_size,
   multi->wsa_event = WSACreateEvent();
   if(multi->wsa_event == WSA_INVALID_EVENT)
     goto error;
-#elif defined(ENABLE_WAKEUP)
+#endif
+#ifdef ENABLE_WAKEUP
   if(Curl_wakeup_init(multi->wakeup_pair, TRUE) < 0) {
     multi->wakeup_pair[0] = CURL_SOCKET_BAD;
     multi->wakeup_pair[1] = CURL_SOCKET_BAD;
@@ -319,6 +320,7 @@ error:
   Curl_ssl_scache_destroy(multi->ssl_scache);
 #endif
   if(multi->admin) {
+    Curl_multi_ev_xfer_done(multi, multi->admin);
     multi->admin->multi = NULL;
     Curl_close(&multi->admin);
   }
@@ -362,6 +364,17 @@ bool Curl_is_connecting(struct Curl_easy *data)
   return data->mstate < MSTATE_DO;
 }
 
+static CURLMcode multi_assess_wakeup(struct Curl_multi *multi)
+{
+#ifdef ENABLE_WAKEUP
+  if(multi->socket_cb)
+    return Curl_multi_ev_assess_xfer(multi, multi->admin);
+#else
+  (void)multi;
+#endif
+  return CURLM_OK;
+}
+
 static CURLMcode multi_xfers_add(struct Curl_multi *multi,
                                  struct Curl_easy *data)
 {
@@ -528,6 +541,12 @@ CURLMcode curl_multi_add_handle(CURLM *m, CURL *d)
     data->set.server_response_timeout;
   multi->admin->set.no_signal = data->set.no_signal;
 
+  mresult = multi_assess_wakeup(multi);
+  if(mresult) {
+    failf(data, "error enabling wakeup listening: %d", mresult);
+    return mresult;
+  }
+
   CURL_TRC_M(data, "added to multi, mid=%u, running=%u, total=%u",
              data->mid, Curl_multi_xfers_running(multi),
              Curl_uint32_tbl_count(&multi->xfers));
@@ -656,9 +675,6 @@ static CURLcode multi_done(struct Curl_easy *data,
 {
   CURLcode result;
   struct connectdata *conn = data->conn;
-  struct multi_done_ctx mdctx;
-
-  memset(&mdctx, 0, sizeof(mdctx));
 
   CURL_TRC_M(data, "multi_done: status: %d prem: %d done: %d",
              (int)status, (int)premature, data->state.done);
@@ -689,7 +705,7 @@ static CURLcode multi_done(struct Curl_easy *data,
   }
 
   /* this calls the protocol-specific function pointer previously set */
-  if(conn->scheme->run->done && (data->mstate >= MSTATE_PROTOCONNECT))
+  if(conn && conn->scheme->run->done && (data->mstate >= MSTATE_PROTOCONNECT))
     result = conn->scheme->run->done(data, status, premature);
   else
     result = status;
@@ -706,17 +722,23 @@ static CURLcode multi_done(struct Curl_easy *data,
   result = Curl_1st_fatal(result, Curl_xfer_write_done(data, premature));
 
   /* Inform connection filters that this transfer is done */
-  Curl_conn_ev_data_done(data, premature);
+  if(conn)
+    Curl_conn_ev_data_done(data, premature);
 
   process_pending_handles(data->multi); /* connection / multiplex */
 
   if(!result)
     result = Curl_req_done(&data->req, data, premature);
 
-  /* Under the potential connection pool's share lock, decide what to
-   * do with the transfer's connection. */
-  mdctx.premature = premature;
-  Curl_cpool_do_locked(data, data->conn, multi_done_locked, &mdctx);
+  if(conn) {
+    /* Under the potential connection pool's share lock, decide what to
+     * do with the transfer's connection. */
+    struct multi_done_ctx mdctx;
+
+    memset(&mdctx, 0, sizeof(mdctx));
+    mdctx.premature = premature;
+    Curl_cpool_do_locked(data, data->conn, multi_done_locked, &mdctx);
+  }
 
   /* flush the netrc cache */
   Curl_netrc_cleanup(&data->state.netrc);
@@ -871,6 +893,12 @@ CURLMcode curl_multi_remove_handle(CURLM *m, CURL *d)
   if(mresult)
     return mresult;
 
+  mresult = multi_assess_wakeup(multi);
+  if(mresult) {
+    failf(data, "error enabling wakeup listening: %d", mresult);
+    return mresult;
+  }
+
   CURL_TRC_M(data, "removed from multi, mid=%u, running=%u, total=%u",
              mid, Curl_multi_xfers_running(multi),
              Curl_uint32_tbl_count(&multi->xfers));
@@ -1086,75 +1114,79 @@ static CURLcode mstate_perform_pollset(struct Curl_easy *data,
 CURLMcode Curl_multi_pollset(struct Curl_easy *data,
                              struct easy_pollset *ps)
 {
-  CURLMcode mresult = CURLM_OK;
   CURLcode result = CURLE_OK;
 
+  Curl_pollset_reset(ps);
+#ifdef ENABLE_WAKEUP
+  /* The admin handle always listens on the wakeup socket when there
+   * are transfers alive. */
+  if(data->multi && (data == data->multi->admin) &&
+     data->multi->xfers_alive &&
+     (data->multi->wakeup_pair[0] != CURL_SOCKET_BAD)) {
+    result = Curl_pollset_add_in(data, ps, data->multi->wakeup_pair[0]);
+  }
+#endif
   /* If the transfer has no connection, this is fine. Happens when
      called via curl_multi_remove_handle() => Curl_multi_ev_assess() =>
      Curl_multi_pollset(). */
-  Curl_pollset_reset(ps);
-  if(!data->conn)
-    return CURLM_OK;
+  if(!result && data->conn) {
+    switch(data->mstate) {
+    case MSTATE_INIT:
+    case MSTATE_PENDING:
+    case MSTATE_SETUP:
+    case MSTATE_CONNECT:
+      /* nothing to poll for yet */
+      break;
 
-  switch(data->mstate) {
-  case MSTATE_INIT:
-  case MSTATE_PENDING:
-  case MSTATE_SETUP:
-  case MSTATE_CONNECT:
-    /* nothing to poll for yet */
-    break;
+    case MSTATE_RESOLVING:
+      result = Curl_resolv_pollset(data, ps);
+      break;
 
-  case MSTATE_RESOLVING:
-    result = Curl_resolv_pollset(data, ps);
-    break;
+    case MSTATE_CONNECTING:
+      result = mstate_connecting_pollset(data, ps);
+      break;
 
-  case MSTATE_CONNECTING:
-    result = mstate_connecting_pollset(data, ps);
-    break;
+    case MSTATE_PROTOCONNECT:
+    case MSTATE_PROTOCONNECTING:
+      result = mstate_protocol_pollset(data, ps);
+      break;
 
-  case MSTATE_PROTOCONNECT:
-  case MSTATE_PROTOCONNECTING:
-    result = mstate_protocol_pollset(data, ps);
-    break;
+    case MSTATE_DO:
+    case MSTATE_DOING:
+      result = mstate_do_pollset(data, ps);
+      break;
 
-  case MSTATE_DO:
-  case MSTATE_DOING:
-    result = mstate_do_pollset(data, ps);
-    break;
+    case MSTATE_DOING_MORE:
+      result = mstate_domore_pollset(data, ps);
+      break;
 
-  case MSTATE_DOING_MORE:
-    result = mstate_domore_pollset(data, ps);
-    break;
+    case MSTATE_DID: /* same as PERFORMING in regard to polling */
+    case MSTATE_PERFORMING:
+      result = mstate_perform_pollset(data, ps);
+      break;
 
-  case MSTATE_DID: /* same as PERFORMING in regard to polling */
-  case MSTATE_PERFORMING:
-    result = mstate_perform_pollset(data, ps);
-    break;
+    case MSTATE_RATELIMITING:
+      /* we need to let time pass, ignore socket(s) */
+      break;
 
-  case MSTATE_RATELIMITING:
-    /* we need to let time pass, ignore socket(s) */
-    break;
+    case MSTATE_DONE:
+    case MSTATE_COMPLETED:
+    case MSTATE_MSGSENT:
+      /* nothing more to poll for */
+      break;
 
-  case MSTATE_DONE:
-  case MSTATE_COMPLETED:
-  case MSTATE_MSGSENT:
-    /* nothing more to poll for */
-    break;
-
-  default:
-    failf(data, "multi_getsock: unexpected multi state %d", data->mstate);
-    DEBUGASSERT(0);
-    break;
+    default:
+      failf(data, "multi_getsock: unexpected multi state %d", data->mstate);
+      DEBUGASSERT(0);
+      break;
+    }
   }
 
   if(result) {
     if(result == CURLE_OUT_OF_MEMORY)
-      mresult = CURLM_OUT_OF_MEMORY;
-    else {
-      failf(data, "error determining pollset: %d", result);
-      mresult = CURLM_INTERNAL_ERROR;
-    }
-    goto out;
+      return CURLM_OUT_OF_MEMORY;
+    failf(data, "error determining pollset: %d", result);
+    return CURLM_INTERNAL_ERROR;
   }
 
 #ifdef CURLVERBOSE
@@ -1193,8 +1225,7 @@ CURLMcode Curl_multi_pollset(struct Curl_easy *data,
   }
 #endif
 
-out:
-  return mresult;
+  return CURLM_OK;
 }
 
 CURLMcode curl_multi_fdset(CURLM *m,
@@ -1313,7 +1344,176 @@ static void reset_socket_fdwrite(curl_socket_t s)
   if(!getsockopt(s, SOL_SOCKET, SO_TYPE, (char *)&t, &l) && t == SOCK_STREAM)
     swrite(s, NULL, 0);
 }
-#endif
+
+static CURLMcode multi_winsock_select(struct Curl_multi *multi,
+                                      struct curl_pollfds *cpfds,
+                                      unsigned int curl_nfds,
+                                      struct curl_waitfd extra_fds[],
+                                      unsigned int extra_nfds,
+                                      int timeout_ms,
+                                      bool wait_on_nop,
+                                      int *pnevents)
+{
+  CURLMcode mresult = CURLM_OK;
+  WSANETWORKEVENTS wsa_events;
+  int nevents = 0;
+  size_t i;
+
+  DEBUGASSERT(multi->wsa_event != WSA_INVALID_EVENT);
+
+  /* Set the WSA events based on the collected pollds */
+  for(i = 0; i < cpfds->n; i++) {
+    long mask = 0;
+    if(cpfds->pfds[i].events & POLLIN)
+      mask |= FD_READ | FD_ACCEPT | FD_CLOSE;
+    if(cpfds->pfds[i].events & POLLPRI)
+      mask |= FD_OOB;
+    if(cpfds->pfds[i].events & POLLOUT) {
+      mask |= FD_WRITE | FD_CONNECT | FD_CLOSE;
+      reset_socket_fdwrite(cpfds->pfds[i].fd);
+    }
+    if(mask) {
+      if(WSAEventSelect(cpfds->pfds[i].fd, multi->wsa_event, mask) != 0) {
+        mresult = CURLM_OUT_OF_MEMORY;
+        goto out;
+      }
+    }
+  }
+
+  if(cpfds->n || wait_on_nop) {
+    int pollrc = 0;
+
+    if(cpfds->n) {         /* pre-check with Winsock */
+      pollrc = Curl_poll(cpfds->pfds, cpfds->n, 0);
+      if(pollrc < 0) {
+        mresult = CURLM_UNRECOVERABLE_POLL;
+        goto out;
+      }
+      nevents = pollrc;
+    }
+
+    if(!nevents) {
+      /* now wait... if not ready during the pre-check (pollrc == 0) */
+      WSAWaitForMultipleEvents(1, &multi->wsa_event, FALSE, (DWORD)timeout_ms,
+                               FALSE);
+    }
+
+    /* With Winsock, we have to run the following section unconditionally
+       to call WSAEventSelect(fd, event, 0) on all the sockets */
+    /* copy revents results from the poll to the curl_multi_wait poll
+       struct, the bit values of the actual underlying poll() implementation
+       may not be the same as the ones in the public libcurl API! */
+    for(i = 0; i < extra_nfds; i++) {
+      unsigned short mask = 0;
+      curl_socket_t s = extra_fds[i].fd;
+
+      wsa_events.lNetworkEvents = 0;
+      if(WSAEnumNetworkEvents(s, NULL, &wsa_events) == 0) {
+        if(wsa_events.lNetworkEvents & (FD_READ | FD_ACCEPT | FD_CLOSE))
+          mask |= CURL_WAIT_POLLIN;
+        if(wsa_events.lNetworkEvents & (FD_WRITE | FD_CONNECT | FD_CLOSE))
+          mask |= CURL_WAIT_POLLOUT;
+        if(wsa_events.lNetworkEvents & FD_OOB)
+          mask |= CURL_WAIT_POLLPRI;
+        if(!pollrc && wsa_events.lNetworkEvents)
+          nevents++;
+      }
+      WSAEventSelect(s, multi->wsa_event, 0);
+      if(!pollrc) {
+        extra_fds[i].revents = (short)mask;
+        continue;
+      }
+      else {
+        unsigned r = (unsigned)cpfds->pfds[curl_nfds + i].revents;
+        if(r & POLLIN)
+          mask |= CURL_WAIT_POLLIN;
+        if(r & POLLOUT)
+          mask |= CURL_WAIT_POLLOUT;
+        if(r & POLLPRI)
+          mask |= CURL_WAIT_POLLPRI;
+        extra_fds[i].revents = (short)mask;
+      }
+    }
+
+    /* Count up all our own sockets that had activity,
+       and remove them from the event. */
+    for(i = 0; i < curl_nfds; ++i) {
+      wsa_events.lNetworkEvents = 0;
+      if(WSAEnumNetworkEvents(cpfds->pfds[i].fd, NULL, &wsa_events) == 0) {
+        if(!pollrc && wsa_events.lNetworkEvents)
+          nevents++;
+      }
+      WSAEventSelect(cpfds->pfds[i].fd, multi->wsa_event, 0);
+    }
+    WSAResetEvent(multi->wsa_event);
+  }
+
+out:
+  *pnevents = nevents;
+  return mresult;
+}
+
+#else /* USE_WINSOCK */
+
+static CURLMcode multi_posix_poll(struct Curl_multi *multi,
+                                  struct curl_pollfds *cpfds,
+                                  unsigned int curl_nfds,
+                                  struct curl_waitfd extra_fds[],
+                                  unsigned int extra_nfds,
+                                  int timeout_ms,
+                                  bool wait_on_nop,
+                                  int *pnevents)
+{
+  CURLMcode mresult = CURLM_OK;
+  int nevents = 0;
+  size_t i;
+
+  if(cpfds->n) {
+    int pollrc = Curl_poll(cpfds->pfds, cpfds->n, timeout_ms); /* wait... */
+    if(pollrc < 0) {
+      mresult = CURLM_UNRECOVERABLE_POLL;
+      goto out;
+    }
+    nevents = pollrc;
+
+    /* copy revents results from the poll to the curl_multi_wait poll
+       struct, the bit values of the actual underlying poll() implementation
+       may not be the same as the ones in the public libcurl API! */
+    for(i = 0; i < extra_nfds; i++) {
+      unsigned r = (unsigned)cpfds->pfds[curl_nfds + i].revents;
+      unsigned short mask = 0;
+      if(r & POLLIN)
+        mask |= CURL_WAIT_POLLIN;
+      if(r & POLLOUT)
+        mask |= CURL_WAIT_POLLOUT;
+      if(r & POLLPRI)
+        mask |= CURL_WAIT_POLLPRI;
+      extra_fds[i].revents = (short)mask;
+    }
+  }
+  else if(wait_on_nop) {
+    struct curltime expire_time;
+    long sleep_ms = 0;
+
+    /* Avoid busy-looping when there is nothing particular to wait for */
+    multi_timeout(multi, &expire_time, &sleep_ms);
+    if(sleep_ms) {
+      if(sleep_ms > timeout_ms)
+        sleep_ms = timeout_ms;
+      /* when there are no easy handles in the multi, this holds a -1
+         timeout */
+      else if(sleep_ms < 0)
+        sleep_ms = timeout_ms;
+      curlx_wait_ms(sleep_ms);
+    }
+  }
+
+out:
+  *pnevents = nevents;
+  return mresult;
+}
+
+#endif /* !USE_WINSOCK */
 
 #define NUM_POLLS_ON_STACK 10
 
@@ -1322,13 +1522,13 @@ static CURLMcode multi_wait(struct Curl_multi *multi,
                             unsigned int extra_nfds,
                             int timeout_ms,
                             int *ret,
-                            bool extrawait, /* when no socket, wait */
-                            bool use_wakeup)
+                            bool wait_on_nop) /* spend time, even if there
+                                               * is nothing to monitor */
 {
   size_t i;
   struct curltime expire_time;
   long timeout_internal;
-  int retcode = 0;
+  int nevents = 0;
   struct easy_pollset ps;
   struct pollfd a_few_on_stack[NUM_POLLS_ON_STACK];
   struct curl_pollfds cpfds;
@@ -1336,13 +1536,8 @@ static CURLMcode multi_wait(struct Curl_multi *multi,
   struct Curl_easy *data = NULL;
   CURLMcode mresult = CURLM_OK;
   uint32_t mid;
-
-#ifdef USE_WINSOCK
-  WSANETWORKEVENTS wsa_events;
-  DEBUGASSERT(multi->wsa_event != WSA_INVALID_EVENT);
-#endif
-#ifndef ENABLE_WAKEUP
-  (void)use_wakeup;
+#ifdef ENABLE_WAKEUP
+  int wakeup_idx = -1;
 #endif
 
   if(!GOOD_MULTI_HANDLE(multi))
@@ -1380,6 +1575,16 @@ static CURLMcode multi_wait(struct Curl_multi *multi,
     goto out;
   }
 
+#ifdef ENABLE_WAKEUP
+  if(wait_on_nop && multi->wakeup_pair[0] != CURL_SOCKET_BAD) {
+    wakeup_idx = cpfds.n;
+    if(Curl_pollfds_add_sock(&cpfds, multi->wakeup_pair[0], POLLIN)) {
+      mresult = CURLM_OUT_OF_MEMORY;
+      goto out;
+    }
+  }
+#endif
+
   curl_nfds = cpfds.n; /* what curl internally uses in cpfds */
   /* Add external file descriptions from poll-like struct curl_waitfd */
   for(i = 0; i < extra_nfds; i++) {
@@ -1396,38 +1601,6 @@ static CURLMcode multi_wait(struct Curl_multi *multi,
     }
   }
 
-#ifdef USE_WINSOCK
-  /* Set the WSA events based on the collected pollds */
-  for(i = 0; i < cpfds.n; i++) {
-    long mask = 0;
-    if(cpfds.pfds[i].events & POLLIN)
-      mask |= FD_READ | FD_ACCEPT | FD_CLOSE;
-    if(cpfds.pfds[i].events & POLLPRI)
-      mask |= FD_OOB;
-    if(cpfds.pfds[i].events & POLLOUT) {
-      mask |= FD_WRITE | FD_CONNECT | FD_CLOSE;
-      reset_socket_fdwrite(cpfds.pfds[i].fd);
-    }
-    if(mask) {
-      if(WSAEventSelect(cpfds.pfds[i].fd, multi->wsa_event, mask) != 0) {
-        mresult = CURLM_OUT_OF_MEMORY;
-        goto out;
-      }
-    }
-  }
-#endif
-
-#ifdef ENABLE_WAKEUP
-#ifndef USE_WINSOCK
-  if(use_wakeup && multi->wakeup_pair[0] != CURL_SOCKET_BAD) {
-    if(Curl_pollfds_add_sock(&cpfds, multi->wakeup_pair[0], POLLIN)) {
-      mresult = CURLM_OUT_OF_MEMORY;
-      goto out;
-    }
-  }
-#endif
-#endif
-
   /* We check the internal timeout *AFTER* we collected all sockets to
    * poll. Collecting the sockets may install new timers by protocols
    * and connection filters.
@@ -1439,122 +1612,32 @@ static CURLMcode multi_wait(struct Curl_multi *multi,
   if(data)
     CURL_TRC_M(data, "multi_wait(fds=%d, timeout=%d) tinternal=%ld",
                cpfds.n, timeout_ms, timeout_internal);
-#if defined(ENABLE_WAKEUP) && defined(USE_WINSOCK)
-  if(cpfds.n || use_wakeup) {
-#else
-  if(cpfds.n) {
-#endif
-    int pollrc;
-#ifdef USE_WINSOCK
-    if(cpfds.n)         /* pre-check with Winsock */
-      pollrc = Curl_poll(cpfds.pfds, cpfds.n, 0);
-    else
-      pollrc = 0;
-#else
-    pollrc = Curl_poll(cpfds.pfds, cpfds.n, timeout_ms); /* wait... */
-#endif
-    if(pollrc < 0) {
-      mresult = CURLM_UNRECOVERABLE_POLL;
-      goto out;
-    }
-
-    if(pollrc > 0) {
-      retcode = pollrc;
-#ifdef USE_WINSOCK
-    }
-    else { /* now wait... if not ready during the pre-check (pollrc == 0) */
-      WSAWaitForMultipleEvents(1, &multi->wsa_event, FALSE, (DWORD)timeout_ms,
-                               FALSE);
-    }
-    /* With Winsock, we have to run the following section unconditionally
-       to call WSAEventSelect(fd, event, 0) on all the sockets */
-    {
-#endif
-      /* copy revents results from the poll to the curl_multi_wait poll
-         struct, the bit values of the actual underlying poll() implementation
-         may not be the same as the ones in the public libcurl API! */
-      for(i = 0; i < extra_nfds; i++) {
-        unsigned r = (unsigned)cpfds.pfds[curl_nfds + i].revents;
-        unsigned short mask = 0;
-#ifdef USE_WINSOCK
-        curl_socket_t s = extra_fds[i].fd;
-        wsa_events.lNetworkEvents = 0;
-        if(WSAEnumNetworkEvents(s, NULL, &wsa_events) == 0) {
-          if(wsa_events.lNetworkEvents & (FD_READ | FD_ACCEPT | FD_CLOSE))
-            mask |= CURL_WAIT_POLLIN;
-          if(wsa_events.lNetworkEvents & (FD_WRITE | FD_CONNECT | FD_CLOSE))
-            mask |= CURL_WAIT_POLLOUT;
-          if(wsa_events.lNetworkEvents & FD_OOB)
-            mask |= CURL_WAIT_POLLPRI;
-          if(ret && !pollrc && wsa_events.lNetworkEvents)
-            retcode++;
-        }
-        WSAEventSelect(s, multi->wsa_event, 0);
-        if(!pollrc) {
-          extra_fds[i].revents = (short)mask;
-          continue;
-        }
-#endif
-        if(r & POLLIN)
-          mask |= CURL_WAIT_POLLIN;
-        if(r & POLLOUT)
-          mask |= CURL_WAIT_POLLOUT;
-        if(r & POLLPRI)
-          mask |= CURL_WAIT_POLLPRI;
-        extra_fds[i].revents = (short)mask;
-      }
 
 #ifdef USE_WINSOCK
-      /* Count up all our own sockets that had activity,
-         and remove them from the event. */
-      for(i = 0; i < curl_nfds; ++i) {
-        wsa_events.lNetworkEvents = 0;
-        if(WSAEnumNetworkEvents(cpfds.pfds[i].fd, NULL, &wsa_events) == 0) {
-          if(ret && !pollrc && wsa_events.lNetworkEvents)
-            retcode++;
-        }
-        WSAEventSelect(cpfds.pfds[i].fd, multi->wsa_event, 0);
-      }
-      WSAResetEvent(multi->wsa_event);
+  mresult = multi_winsock_select(multi, &cpfds, curl_nfds,
+                                 extra_fds, extra_nfds,
+                                 timeout_ms, wait_on_nop, &nevents);
 #else
+  mresult = multi_posix_poll(multi, &cpfds, curl_nfds,
+                             extra_fds, extra_nfds,
+                             timeout_ms, wait_on_nop, &nevents);
+#endif
+
 #ifdef ENABLE_WAKEUP
-      if(use_wakeup && multi->wakeup_pair[0] != CURL_SOCKET_BAD) {
-        if(cpfds.pfds[curl_nfds + extra_nfds].revents & POLLIN) {
-          (void)Curl_wakeup_consume(multi->wakeup_pair, TRUE);
-          /* do not count the wakeup socket into the returned value */
-          retcode--;
-        }
+    if(nevents && (wakeup_idx >= 0)) {
+      if(cpfds.pfds[wakeup_idx].revents & POLLIN) {
+        (void)Curl_wakeup_consume(multi->wakeup_pair, TRUE);
+        /* do not count the wakeup socket into the returned value */
+        nevents--;
       }
-#endif
-#endif
     }
-  }
-
-  if(ret)
-    *ret = retcode;
-#if defined(ENABLE_WAKEUP) && defined(USE_WINSOCK)
-  if(extrawait && !cpfds.n && !use_wakeup) {
-#else
-  if(extrawait && !cpfds.n) {
 #endif
-    long sleep_ms = 0;
-
-    /* Avoid busy-looping when there is nothing particular to wait for */
-    multi_timeout(multi, &expire_time, &sleep_ms);
-    if(sleep_ms) {
-      if(sleep_ms > timeout_ms)
-        sleep_ms = timeout_ms;
-      /* when there are no easy handles in the multi, this holds a -1
-         timeout */
-      else if(sleep_ms < 0)
-        sleep_ms = timeout_ms;
-      curlx_wait_ms(sleep_ms);
-    }
-  }
 
 out:
   Curl_pollset_cleanup(&ps);
   Curl_pollfds_cleanup(&cpfds);
+  if(ret)
+    *ret = nevents;
   return mresult;
 }
 
@@ -1564,8 +1647,7 @@ CURLMcode curl_multi_wait(CURLM *multi,
                           int timeout_ms,
                           int *ret)
 {
-  return multi_wait(multi, extra_fds, extra_nfds, timeout_ms, ret, FALSE,
-                    FALSE);
+  return multi_wait(multi, extra_fds, extra_nfds, timeout_ms, ret, FALSE);
 }
 
 CURLMcode curl_multi_poll(CURLM *multi,
@@ -1574,7 +1656,7 @@ CURLMcode curl_multi_poll(CURLM *multi,
                           int timeout_ms,
                           int *ret)
 {
-  return multi_wait(multi, extra_fds, extra_nfds, timeout_ms, ret, TRUE, TRUE);
+  return multi_wait(multi, extra_fds, extra_nfds, timeout_ms, ret, TRUE);
 }
 
 CURLMcode curl_multi_wakeup(CURLM *m)
@@ -1588,11 +1670,11 @@ CURLMcode curl_multi_wakeup(CURLM *m)
   if(!GOOD_MULTI_HANDLE(multi))
     return CURLM_BAD_HANDLE;
 
-#ifdef ENABLE_WAKEUP
 #ifdef USE_WINSOCK
   if(WSASetEvent(multi->wsa_event))
     return CURLM_OK;
-#else
+#endif
+#ifdef ENABLE_WAKEUP
   /* the wakeup_pair variable is only written during init and cleanup,
      making it safe to access from another thread after the init part
      and before cleanup */
@@ -1601,7 +1683,6 @@ CURLMcode curl_multi_wakeup(CURLM *m)
       return CURLM_WAKEUP_FAILURE;
     return CURLM_OK;
   }
-#endif
 #endif
   return CURLM_WAKEUP_FAILURE;
 }
@@ -2408,6 +2489,8 @@ static void handle_completed(struct Curl_multi *multi,
   Curl_uint32_bset_remove(&multi->pending, data->mid);
   Curl_uint32_bset_add(&multi->msgsent, data->mid);
   --multi->xfers_alive;
+  if(!multi->xfers_alive)
+    multi_assess_wakeup(multi);
 }
 
 static CURLMcode multi_runsingle(struct Curl_multi *multi,
@@ -2890,10 +2973,9 @@ CURLMcode curl_multi_cleanup(CURLM *m)
 
 #ifdef USE_WINSOCK
     WSACloseEvent(multi->wsa_event);
-#else
+#endif
 #ifdef ENABLE_WAKEUP
   Curl_wakeup_destroy(multi->wakeup_pair);
-#endif
 #endif
 
     multi_xfer_bufs_free(multi);
@@ -3132,6 +3214,14 @@ static CURLMcode multi_socket(struct Curl_multi *multi,
        handles the case when the application asks libcurl to run the timeout
        prematurely. */
     memset(&multi->last_expire_ts, 0, sizeof(multi->last_expire_ts));
+
+    /* Applications may set `socket_cb` *after* having added transfers
+     * first. *Then* kick off processing with a
+     * curl_multi_socket_action(TIMEOUT) afterwards. Make sure our
+     * admin handle registers its pollset with the callbacks present. */
+    mresult = multi_assess_wakeup(multi);
+    if(mresult)
+      goto out;
   }
 
   multi_mark_expired_as_dirty(multi, multi_now(multi));
diff --git a/lib/multi_ev.c b/lib/multi_ev.c
index 696a012ebf..b98cda0c68 100644
--- a/lib/multi_ev.c
+++ b/lib/multi_ev.c
@@ -603,10 +603,8 @@ void Curl_multi_ev_xfer_done(struct Curl_multi *multi,
                              struct Curl_easy *data)
 {
   DEBUGASSERT(!data->conn); /* transfer should have been detached */
-  if(data != multi->admin) {
-    (void)mev_assess(multi, data, NULL);
-    Curl_meta_remove(data, CURL_META_MEV_POLLSET);
-  }
+  (void)mev_assess(multi, data, NULL);
+  Curl_meta_remove(data, CURL_META_MEV_POLLSET);
 }
 
 void Curl_multi_ev_conn_done(struct Curl_multi *multi,
diff --git a/lib/multihandle.h b/lib/multihandle.h
index 7a561124ae..3b18930e00 100644
--- a/lib/multihandle.h
+++ b/lib/multihandle.h
@@ -71,7 +71,7 @@ typedef enum {
 
 #define CURLPIPE_ANY (CURLPIPE_MULTIPLEX)
 
-#ifndef CURL_DISABLE_SOCKETPAIR
+#if !defined(CURL_DISABLE_SOCKETPAIR) && !defined(USE_WINSOCK)
 #define ENABLE_WAKEUP
 #endif
 
@@ -160,12 +160,11 @@ struct Curl_multi {
 
 #ifdef USE_WINSOCK
   WSAEVENT wsa_event; /* Winsock event used for waits */
-#else
+#endif
 #ifdef ENABLE_WAKEUP
   curl_socket_t wakeup_pair[2]; /* eventfd()/pipe()/socketpair() used for
                                    wakeup 0 is used for read, 1 is used
                                    for write */
-#endif
 #endif
   unsigned int max_concurrent_streams;
   unsigned int maxconnects; /* if >0, a fixed limit of the maximum number of
diff --git a/tests/http/test_19_shutdown.py b/tests/http/test_19_shutdown.py
index 7cb8ce6415..9e5effd20c 100644
--- a/tests/http/test_19_shutdown.py
+++ b/tests/http/test_19_shutdown.py
@@ -160,7 +160,7 @@ class TestShutdown:
         # check that all connection sockets were removed from event
         removes = [line for line in r.trace_lines
                    if re.match(r'.*socket cb: socket \d+ REMOVED', line)]
-        assert len(removes) == count, f'{removes}'
+        assert len(removes) >= count, f'{removes}'
 
     # check graceful shutdown on multiplexed http
     @pytest.mark.parametrize("proto", Env.http_mplx_protos())
diff --git a/tests/libtest/lib2405.c b/tests/libtest/lib2405.c
index f19a7ee4e1..d65196e236 100644
--- a/tests/libtest/lib2405.c
+++ b/tests/libtest/lib2405.c
@@ -331,8 +331,8 @@ static CURLcode empty_multi_test(void)
     goto test_cleanup;
   }
   else if(fd_count > 0) {
-    curl_mfprintf(stderr, "curl_multi_waitfds() returned non-zero count of "
-                  "waitfds: %d.\n", fd_count);
+    curl_mfprintf(stderr, "curl_multi_waitfds(), empty, returned non-zero "
+                  "count of waitfds: %d.\n", fd_count);
     result = TEST_ERR_FAILURE;
     goto test_cleanup;
   }
@@ -352,8 +352,8 @@ static CURLcode empty_multi_test(void)
     result = TEST_ERR_FAILURE;
     goto test_cleanup;
   }
-  else if(fd_count > 0) {
-    curl_mfprintf(stderr, "curl_multi_waitfds() returned non-zero count of "
+  else if(fd_count > 1) {
+    curl_mfprintf(stderr, "curl_multi_waitfds() returned > 1 count of "
                   "waitfds: %d.\n", fd_count);
     result = TEST_ERR_FAILURE;
     goto test_cleanup;
@@ -380,16 +380,16 @@ static CURLcode test_lib2405(const char *URL)
     goto test_cleanup;
 
   if(testnum == 2405) {
-    /* HTTP1, expected 2 waitfds - one for each transfer */
-    test_run_check(TEST_USE_HTTP1, 2);
+    /* HTTP1, expected 3 waitfds - one for each transfer  + wakeup */
+    test_run_check(TEST_USE_HTTP1, 3);
   }
 #ifdef USE_HTTP2
   else { /* 2407 */
-    /* HTTP2, expected 2 waitfds - one for each transfer */
-    test_run_check(TEST_USE_HTTP2, 2);
+    /* HTTP2, expected 3 waitfds - one for each transfer + wakeup */
+    test_run_check(TEST_USE_HTTP2, 3);
 
-    /* HTTP2 with multiplexing, expected 1 waitfds - one for all transfers */
-    test_run_check(TEST_USE_HTTP2_MPLEX, 1);
+    /* HTTP2 with multiplexing, expected 2 waitfds - transfers + wakeup */
+    test_run_check(TEST_USE_HTTP2_MPLEX, 2);
   }
 #endif
 
diff --git a/tests/libtest/lib530.c b/tests/libtest/lib530.c
index ad2ad536f7..31cef1b702 100644
--- a/tests/libtest/lib530.c
+++ b/tests/libtest/lib530.c
@@ -404,11 +404,11 @@ static CURLcode test_lib530(const char *URL)
   if(!result)
     curl_mfprintf(stderr, "%s FAILED: %d\n", t530_tag(), result);
 
-  result = testone(URL, 0, 1); /* fail 1st call to socket callback */
+  result = testone(URL, 0, 2); /* fail 2nd call to socket callback */
   if(!result)
     curl_mfprintf(stderr, "%s FAILED: %d\n", t530_tag(), result);
 
-  result = testone(URL, 0, 2); /* fail 2nd call to socket callback */
+  result = testone(URL, 0, 3); /* fail 3rd call to socket callback */
   if(!result)
     curl_mfprintf(stderr, "%s FAILED: %d\n", t530_tag(), result);
 
diff --git a/tests/libtest/lib758.c b/tests/libtest/lib758.c
index e743da7f58..b6642cb130 100644
--- a/tests/libtest/lib758.c
+++ b/tests/libtest/lib758.c
@@ -386,7 +386,8 @@ static CURLcode t758_one(const char *URL, int timer_fail_at,
 
     if(t758_ctx.fake_async_cert_verification_pending &&
        !t758_ctx.fake_async_cert_verification_finished) {
-      if(sockets.read.count || sockets.write.count) {
+      /* the wakeup socket will be monitored */
+      if((sockets.read.count > 1) || sockets.write.count) {
         t758_msg("during verification there should be no sockets scheduled");
         result = TEST_ERR_MAJOR_BAD;
         goto test_cleanup;