diff --git a/lib/multiif.h b/lib/multiif.h
index e61c5c6f2c9fd0a80d2a7a608357d944b6dd2c16..15163da985d67889ca51d5d0bcecfa35b3bc2dbe 100644
--- a/lib/multiif.h
+++ b/lib/multiif.h
@@ -30,6 +30,8 @@
 #define MULTI_TIMEOUT_INACCURACY 3000
 #endif
 
+#define MULTI_TIMEOUT_INACCURACY_MS (MULTI_TIMEOUT_INACCURACY / 1000)
+
 /*
  * Prototypes for library-wide functions provided by multi.c
  */
diff --git a/lib/transfer.c b/lib/transfer.c
index 533e394b6bff6e6e66d1393210368c6fe3a708ee..e3194415b7bcbf7cdf7fe761ded7d8ef04c14637 100644
--- a/lib/transfer.c
+++ b/lib/transfer.c
@@ -1309,10 +1309,11 @@ CURLcode Curl_pretransfer(struct SessionHandle *data)
     Curl_pgrsStartNow(data);
 
     if(data->set.timeout)
-      Curl_expire(data, data->set.timeout);
+      Curl_expire(data, data->set.timeout + MULTI_TIMEOUT_INACCURACY_MS);
 
     if(data->set.connecttimeout)
-      Curl_expire(data, data->set.connecttimeout);
+      Curl_expire(data, data->set.connecttimeout +
+                  MULTI_TIMEOUT_INACCURACY_MS);
 
     /* In case the handle is re-used and an authentication method was picked
        in the session we need to make sure we only use the one(s) we now