diff --git a/lib/asyn-thread.c b/lib/asyn-thread.c
index 36735fc60..3ab253d8c 100644
--- a/lib/asyn-thread.c
+++ b/lib/asyn-thread.c
@@ -179,7 +179,7 @@ struct thread_sync_data {
 struct thread_data {
   curl_thread_t thread_hnd;
   unsigned int poll_interval;
-  time_t interval_end;
+  timediff_t interval_end;
   struct thread_sync_data tsd;
 };
 
@@ -622,8 +622,8 @@ CURLcode Curl_resolver_is_resolved(struct connectdata *conn,
   else {
     /* poll for name lookup done with exponential backoff up to 250ms */
     /* should be fine even if this converts to 32 bit */
-    time_t elapsed = (time_t)Curl_timediff(Curl_now(),
-                                           data->progress.t_startsingle);
+    timediff_t elapsed = Curl_timediff(Curl_now(),
+                                       data->progress.t_startsingle);
     if(elapsed < 0)
       elapsed = 0;
 
@@ -648,7 +648,7 @@ int Curl_resolver_getsock(struct connectdata *conn,
                           curl_socket_t *socks)
 {
   int ret_val = 0;
-  time_t milli;
+  timediff_t milli;
   timediff_t ms;
   struct Curl_easy *data = conn->data;
   struct resdata *reslv = (struct resdata *)data->state.resolver;
@@ -672,7 +672,7 @@ int Curl_resolver_getsock(struct connectdata *conn,
     if(ms < 3)
       milli = 0;
     else if(ms <= 50)
-      milli = (time_t)ms/3;
+      milli = ms/3;
     else if(ms <= 250)
       milli = 50;
     else
diff --git a/lib/ftp.c b/lib/ftp.c
index 2b439afd7..4f6076e31 100644
--- a/lib/ftp.c
+++ b/lib/ftp.c
@@ -633,8 +633,8 @@ CURLcode Curl_GetFTPResponse(ssize_t *nreadp, /* return number of bytes read */
 
   while(!*ftpcode && !result) {
     /* check and reset timeout value every lap */
-    time_t timeout = Curl_pp_state_timeout(pp, FALSE);
-    time_t interval_ms;
+    timediff_t timeout = Curl_pp_state_timeout(pp, FALSE);
+    timediff_t interval_ms;
 
     if(timeout <= 0) {
       failf(data, "FTP response timeout");
@@ -3252,7 +3252,7 @@ static CURLcode ftp_done(struct connectdata *conn, CURLcode status,
      * data has been transferred. This happens when doing through NATs etc that
      * abandon old silent connections.
      */
-    long old_time = pp->response_time;
+    timediff_t old_time = pp->response_time;
 
     pp->response_time = 60*1000; /* give it only a minute for now */
     pp->response = Curl_now(); /* timeout relative now */
diff --git a/lib/pingpong.c b/lib/pingpong.c
index d0710053b..ced832ecf 100644
--- a/lib/pingpong.c
+++ b/lib/pingpong.c
@@ -5,7 +5,7 @@
  *                            | (__| |_| |  _ <| |___
  *                             \___|\___/|_| \_\_____|
  *
- * Copyright (C) 1998 - 2019, Daniel Stenberg, <daniel@haxx.se>, et al.
+ * Copyright (C) 1998 - 2020, Daniel Stenberg, <daniel@haxx.se>, et al.
  *
  * This software is licensed as described in the file COPYING, which
  * you should have received as part of this distribution. The terms
@@ -44,12 +44,12 @@
 
 /* Returns timeout in ms. 0 or negative number means the timeout has already
    triggered */
-time_t Curl_pp_state_timeout(struct pingpong *pp, bool disconnecting)
+timediff_t Curl_pp_state_timeout(struct pingpong *pp, bool disconnecting)
 {
   struct connectdata *conn = pp->conn;
   struct Curl_easy *data = conn->data;
-  time_t timeout_ms; /* in milliseconds */
-  long response_time = (data->set.server_response_timeout)?
+  timediff_t timeout_ms; /* in milliseconds */
+  timediff_t response_time = (data->set.server_response_timeout)?
     data->set.server_response_timeout: pp->response_time;
 
   /* if CURLOPT_SERVER_RESPONSE_TIMEOUT is set, use that to determine
@@ -60,12 +60,12 @@ time_t Curl_pp_state_timeout(struct pingpong *pp, bool disconnecting)
   /* Without a requested timeout, we only wait 'response_time' seconds for the
      full response to arrive before we bail out */
   timeout_ms = response_time -
-    (time_t)Curl_timediff(Curl_now(), pp->response); /* spent time */
+    Curl_timediff(Curl_now(), pp->response); /* spent time */
 
   if(data->set.timeout && !disconnecting) {
     /* if timeout is requested, find out how much remaining time we have */
-    time_t timeout2_ms = data->set.timeout - /* timeout time */
-      (time_t)Curl_timediff(Curl_now(), conn->now); /* spent time */
+    timediff_t timeout2_ms = data->set.timeout - /* timeout time */
+      Curl_timediff(Curl_now(), conn->now); /* spent time */
 
     /* pick the lowest number */
     timeout_ms = CURLMIN(timeout_ms, timeout2_ms);
@@ -83,8 +83,8 @@ CURLcode Curl_pp_statemach(struct pingpong *pp, bool block,
   struct connectdata *conn = pp->conn;
   curl_socket_t sock = conn->sock[FIRSTSOCKET];
   int rc;
-  time_t interval_ms;
-  time_t timeout_ms = Curl_pp_state_timeout(pp, disconnecting);
+  timediff_t interval_ms;
+  timediff_t timeout_ms = Curl_pp_state_timeout(pp, disconnecting);
   struct Curl_easy *data = conn->data;
   CURLcode result = CURLE_OK;
 
diff --git a/lib/pingpong.h b/lib/pingpong.h
index 849a7c0ff..e874799d4 100644
--- a/lib/pingpong.h
+++ b/lib/pingpong.h
@@ -7,7 +7,7 @@
  *                            | (__| |_| |  _ <| |___
  *                             \___|\___/|_| \_\_____|
  *
- * Copyright (C) 1998 - 2019, Daniel Stenberg, <daniel@haxx.se>, et al.
+ * Copyright (C) 1998 - 2020, Daniel Stenberg, <daniel@haxx.se>, et al.
  *
  * This software is licensed as described in the file COPYING, which
  * you should have received as part of this distribution. The terms
@@ -60,9 +60,8 @@ struct pingpong {
   size_t sendsize; /* total size of the sendthis buffer */
   struct curltime response; /* set to Curl_now() when a command has been sent
                                off, used to time-out response reading */
-  long response_time; /* When no timeout is given, this is the amount of
-                         milliseconds we await for a server response. */
-
+  timediff_t response_time; /* When no timeout is given, this is the amount of
+                               milliseconds we await for a server response. */
   struct connectdata *conn; /* points to the connectdata struct that this
                                belongs to */
 
@@ -89,7 +88,7 @@ void Curl_pp_init(struct pingpong *pp);
 
 /* Returns timeout in ms. 0 or negative number means the timeout has already
    triggered */
-time_t Curl_pp_state_timeout(struct pingpong *pp, bool disconnecting);
+timediff_t Curl_pp_state_timeout(struct pingpong *pp, bool disconnecting);
 
 
 /***********************************************************************
diff --git a/lib/progress.c b/lib/progress.c
index 60a941ab2..895138448 100644
--- a/lib/progress.c
+++ b/lib/progress.c
@@ -5,7 +5,7 @@
  *                            | (__| |_| |  _ <| |___
  *                             \___|\___/|_| \_\_____|
  *
- * Copyright (C) 1998 - 2019, Daniel Stenberg, <daniel@haxx.se>, et al.
+ * Copyright (C) 1998 - 2020, Daniel Stenberg, <daniel@haxx.se>, et al.
  *
  * This software is licensed as described in the file COPYING, which
  * you should have received as part of this distribution. The terms
@@ -282,9 +282,9 @@ timediff_t Curl_pgrsLimitWaitTime(curl_off_t cursize,
    * stay below 'limit'.
    */
   if(size < CURL_OFF_T_MAX/1000)
-    minimum = (time_t) (CURL_OFF_T_C(1000) * size / limit);
+    minimum = (timediff_t) (CURL_OFF_T_C(1000) * size / limit);
   else {
-    minimum = (time_t) (size / limit);
+    minimum = (timediff_t) (size / limit);
     if(minimum < TIMEDIFF_T_MAX/1000)
       minimum *= 1000;
     else
diff --git a/lib/vssh/libssh2.c b/lib/vssh/libssh2.c
index 63663ec46..d54b4ca4b 100644
--- a/lib/vssh/libssh2.c
+++ b/lib/vssh/libssh2.c
@@ -2969,7 +2969,7 @@ static CURLcode ssh_block_statemach(struct connectdata *conn,
         fd_write = sock;
       /* wait for the socket to become ready */
       (void)Curl_socket_check(fd_read, CURL_SOCKET_BAD, fd_write,
-                              left>1000?1000:(time_t)left);
+                              left>1000?1000:left);
     }
 #endif
 
diff --git a/lib/vtls/bearssl.c b/lib/vtls/bearssl.c
index 1a6530c81..628e16a12 100644
--- a/lib/vtls/bearssl.c
+++ b/lib/vtls/bearssl.c
@@ -642,7 +642,7 @@ static CURLcode bearssl_connect_common(struct connectdata *conn,
   struct Curl_easy *data = conn->data;
   struct ssl_connect_data *connssl = &conn->ssl[sockindex];
   curl_socket_t sockfd = conn->sock[sockindex];
-  time_t timeout_ms;
+  timediff_t timeout_ms;
   int what;
 
   /* check if the connection has already been established */
diff --git a/lib/vtls/gskit.c b/lib/vtls/gskit.c
index 4f29a2137..0538e4a46 100644
--- a/lib/vtls/gskit.c
+++ b/lib/vtls/gskit.c
@@ -819,7 +819,7 @@ static CURLcode gskit_connect_step1(struct connectdata *conn, int sockindex)
   if(!result) {
     /* Compute the handshake timeout. Since GSKit granularity is 1 second,
        we round up the required value. */
-    long timeout = Curl_timeleft(data, NULL, TRUE);
+    timediff_t timeout = Curl_timeleft(data, NULL, TRUE);
     if(timeout < 0)
       result = CURLE_OPERATION_TIMEDOUT;
     else
@@ -932,7 +932,7 @@ static CURLcode gskit_connect_step2(struct connectdata *conn, int sockindex,
   /* Poll or wait for end of SSL asynchronous handshake. */
 
   for(;;) {
-    long timeout_ms = nonblocking? 0: Curl_timeleft(data, NULL, TRUE);
+    timediff_t timeout_ms = nonblocking? 0: Curl_timeleft(data, NULL, TRUE);
     if(timeout_ms < 0)
       timeout_ms = 0;
     stmv.tv_sec = timeout_ms / 1000;
diff --git a/lib/vtls/gtls.c b/lib/vtls/gtls.c
index 0bd6c6528..9b4c3659a 100644
--- a/lib/vtls/gtls.c
+++ b/lib/vtls/gtls.c
@@ -235,7 +235,7 @@ static CURLcode handshake(struct connectdata *conn,
 
       what = Curl_socket_check(readfd, CURL_SOCKET_BAD, writefd,
                                nonblocking?0:
-                               timeout_ms?(time_t)timeout_ms:1000);
+                               timeout_ms?timeout_ms:1000);
       if(what < 0) {
         /* fatal error */
         failf(data, "select/poll on SSL socket, errno: %d", SOCKERRNO);
diff --git a/lib/vtls/mbedtls.c b/lib/vtls/mbedtls.c
index 0df6bb4ae..ba31b8e78 100644
--- a/lib/vtls/mbedtls.c
+++ b/lib/vtls/mbedtls.c
@@ -938,7 +938,7 @@ mbed_connect_common(struct connectdata *conn,
         connssl->connecting_state?sockfd:CURL_SOCKET_BAD;
 
       what = Curl_socket_check(readfd, CURL_SOCKET_BAD, writefd,
-                               nonblocking ? 0 : (time_t)timeout_ms);
+                               nonblocking ? 0 : timeout_ms);
       if(what < 0) {
         /* fatal error */
         failf(data, "select/poll on SSL socket, errno: %d", SOCKERRNO);
diff --git a/lib/vtls/mesalink.c b/lib/vtls/mesalink.c
index cab1e390b..7132bdfd2 100644
--- a/lib/vtls/mesalink.c
+++ b/lib/vtls/mesalink.c
@@ -6,7 +6,7 @@
  *                             \___|\___/|_| \_\_____|
  *
  * Copyright (C) 2017 - 2018, Yiming Jing, <jingyiming@baidu.com>
- * Copyright (C) 1998 - 2019, Daniel Stenberg, <daniel@haxx.se>, et al.
+ * Copyright (C) 1998 - 2020, Daniel Stenberg, <daniel@haxx.se>, et al.
  *
  * This software is licensed as described in the file COPYING, which
  * you should have received as part of this distribution. The terms
@@ -542,9 +542,8 @@ mesalink_connect_common(struct connectdata *conn, int sockindex,
                                ? sockfd
                                : CURL_SOCKET_BAD;
 
-      what = Curl_socket_check(
-        readfd, CURL_SOCKET_BAD, writefd,
-        nonblocking ? 0 : (time_t)timeout_ms);
+      what = Curl_socket_check(readfd, CURL_SOCKET_BAD, writefd,
+                               nonblocking ? 0 : timeout_ms);
       if(what < 0) {
         /* fatal error */
         failf(data, "select/poll on SSL socket, errno: %d", SOCKERRNO);
diff --git a/lib/vtls/openssl.c b/lib/vtls/openssl.c
index 56920deed..ec7baf4e2 100644
--- a/lib/vtls/openssl.c
+++ b/lib/vtls/openssl.c
@@ -3929,7 +3929,6 @@ static CURLcode ossl_connect_common(struct connectdata *conn,
   struct Curl_easy *data = conn->data;
   struct ssl_connect_data *connssl = &conn->ssl[sockindex];
   curl_socket_t sockfd = conn->sock[sockindex];
-  timediff_t timeout_ms;
   int what;
 
   /* check if the connection has already been established */
@@ -3940,7 +3939,7 @@ static CURLcode ossl_connect_common(struct connectdata *conn,
 
   if(ssl_connect_1 == connssl->connecting_state) {
     /* Find out how much more time we're allowed */
-    timeout_ms = Curl_timeleft(data, NULL, TRUE);
+    const timediff_t timeout_ms = Curl_timeleft(data, NULL, TRUE);
 
     if(timeout_ms < 0) {
       /* no need to continue if time already is up */
@@ -3958,7 +3957,7 @@ static CURLcode ossl_connect_common(struct connectdata *conn,
         ssl_connect_2_writing == connssl->connecting_state) {
 
     /* check allowed time left */
-    timeout_ms = Curl_timeleft(data, NULL, TRUE);
+    const timediff_t timeout_ms = Curl_timeleft(data, NULL, TRUE);
 
     if(timeout_ms < 0) {
       /* no need to continue if time already is up */
@@ -3976,7 +3975,7 @@ static CURLcode ossl_connect_common(struct connectdata *conn,
         connssl->connecting_state?sockfd:CURL_SOCKET_BAD;
 
       what = Curl_socket_check(readfd, CURL_SOCKET_BAD, writefd,
-                               nonblocking?0:(time_t)timeout_ms);
+                               nonblocking?0:timeout_ms);
       if(what < 0) {
         /* fatal error */
         failf(data, "select/poll on SSL socket, errno: %d", SOCKERRNO);
diff --git a/lib/vtls/schannel.c b/lib/vtls/schannel.c
index a23179eca..1434d9fba 100644
--- a/lib/vtls/schannel.c
+++ b/lib/vtls/schannel.c
@@ -1514,7 +1514,7 @@ schannel_connect_common(struct connectdata *conn, int sockindex,
         connssl->connecting_state ? sockfd : CURL_SOCKET_BAD;
 
       what = Curl_socket_check(readfd, CURL_SOCKET_BAD, writefd,
-                               nonblocking ? 0 : (time_t)timeout_ms);
+                               nonblocking ? 0 : timeout_ms);
       if(what < 0) {
         /* fatal error */
         failf(data, "select/poll on SSL/TLS socket, errno: %d", SOCKERRNO);
@@ -1663,13 +1663,9 @@ schannel_send(struct connectdata *conn, int sockindex,
 
     /* send entire message or fail */
     while(len > (size_t)written) {
-      ssize_t this_write;
-      timediff_t timeout_ms;
+      ssize_t this_write = 0;
       int what;
-
-      this_write = 0;
-
-      timeout_ms = Curl_timeleft(conn->data, NULL, FALSE);
+      timediff_t timeout_ms = Curl_timeleft(conn->data, NULL, FALSE);
       if(timeout_ms < 0) {
         /* we already got the timeout */
         failf(conn->data, "schannel: timed out sending data "
@@ -1678,7 +1674,7 @@ schannel_send(struct connectdata *conn, int sockindex,
         written = -1;
         break;
       }
-      if(!timeout_ms)
+      else if(!timeout_ms)
         timeout_ms = TIMEDIFF_T_MAX;
       what = SOCKET_WRITABLE(conn->sock[sockindex], timeout_ms);
       if(what < 0) {
diff --git a/lib/vtls/sectransp.c b/lib/vtls/sectransp.c
index 135d34cf0..2627aff16 100644
--- a/lib/vtls/sectransp.c
+++ b/lib/vtls/sectransp.c
@@ -2836,7 +2836,6 @@ sectransp_connect_common(struct connectdata *conn,
   struct Curl_easy *data = conn->data;
   struct ssl_connect_data *connssl = &conn->ssl[sockindex];
   curl_socket_t sockfd = conn->sock[sockindex];
-  timediff_t timeout_ms;
   int what;
 
   /* check if the connection has already been established */
@@ -2847,7 +2846,7 @@ sectransp_connect_common(struct connectdata *conn,
 
   if(ssl_connect_1 == connssl->connecting_state) {
     /* Find out how much more time we're allowed */
-    timeout_ms = Curl_timeleft(data, NULL, TRUE);
+    const timediff_t timeout_ms = Curl_timeleft(data, NULL, TRUE);
 
     if(timeout_ms < 0) {
       /* no need to continue if time already is up */
@@ -2865,7 +2864,7 @@ sectransp_connect_common(struct connectdata *conn,
         ssl_connect_2_writing == connssl->connecting_state) {
 
     /* check allowed time left */
-    timeout_ms = Curl_timeleft(data, NULL, TRUE);
+    const timediff_t timeout_ms = Curl_timeleft(data, NULL, TRUE);
 
     if(timeout_ms < 0) {
       /* no need to continue if time already is up */
@@ -2883,7 +2882,7 @@ sectransp_connect_common(struct connectdata *conn,
       connssl->connecting_state?sockfd:CURL_SOCKET_BAD;
 
       what = Curl_socket_check(readfd, CURL_SOCKET_BAD, writefd,
-                               nonblocking?0:(time_t)timeout_ms);
+                               nonblocking ? 0 : timeout_ms);
       if(what < 0) {
         /* fatal error */
         failf(data, "select/poll on SSL socket, errno: %d", SOCKERRNO);
diff --git a/lib/vtls/wolfssl.c b/lib/vtls/wolfssl.c
index 8f7dd3abd..f5f13fc02 100644
--- a/lib/vtls/wolfssl.c
+++ b/lib/vtls/wolfssl.c
@@ -944,7 +944,6 @@ wolfssl_connect_common(struct connectdata *conn,
   struct Curl_easy *data = conn->data;
   struct ssl_connect_data *connssl = &conn->ssl[sockindex];
   curl_socket_t sockfd = conn->sock[sockindex];
-  time_t timeout_ms;
   int what;
 
   /* check if the connection has already been established */
@@ -955,7 +954,7 @@ wolfssl_connect_common(struct connectdata *conn,
 
   if(ssl_connect_1 == connssl->connecting_state) {
     /* Find out how much more time we're allowed */
-    timeout_ms = Curl_timeleft(data, NULL, TRUE);
+    const timediff_t timeout_ms = Curl_timeleft(data, NULL, TRUE);
 
     if(timeout_ms < 0) {
       /* no need to continue if time already is up */
@@ -973,7 +972,7 @@ wolfssl_connect_common(struct connectdata *conn,
         ssl_connect_2_writing == connssl->connecting_state) {
 
     /* check allowed time left */
-    timeout_ms = Curl_timeleft(data, NULL, TRUE);
+    const timediff_t timeout_ms = Curl_timeleft(data, NULL, TRUE);
 
     if(timeout_ms < 0) {
       /* no need to continue if time already is up */