diff --git a/docs/cmdline-opts/retry.d b/docs/cmdline-opts/retry.d
index 32d1c799b..3db89b71c 100644
--- a/docs/cmdline-opts/retry.d
+++ b/docs/cmdline-opts/retry.d
@@ -14,4 +14,7 @@ for all forthcoming retries it will double the waiting time until it reaches
 using --retry-delay you disable this exponential backoff algorithm. See also
 --retry-max-time to limit the total time allowed for retries.
 
+Since curl 7.66.0, curl will comply with the Retry-After: response header if
+one was present to know when to issue the next retry.
+
 If this option is used several times, the last one will be used.
diff --git a/src/tool_operate.c b/src/tool_operate.c
index 923b5a99d..01ee20061 100644
--- a/src/tool_operate.c
+++ b/src/tool_operate.c
@@ -496,6 +496,8 @@ static CURLcode post_transfer(struct GlobalConfig *global,
     }
 
     if(retry) {
+      long sleeptime = 0;
+      curl_off_t retry_after = 0;
       static const char * const m[]={
         NULL,
         "timeout",
@@ -504,13 +506,24 @@ static CURLcode post_transfer(struct GlobalConfig *global,
         "FTP error"
       };
 
+      sleeptime = per->retry_sleep;
+      if(RETRY_HTTP == retry) {
+        curl_easy_getinfo(curl, CURLINFO_RETRY_AFTER, &retry_after);
+        if(retry_after) {
+          /* store in a 'long', make sure it doesn't overflow */
+          if(retry_after > LONG_MAX/1000)
+            sleeptime = LONG_MAX;
+          else
+            sleeptime = (long)retry_after * 1000; /* milliseconds */
+        }
+      }
       warnf(config->global, "Transient problem: %s "
             "Will retry in %ld seconds. "
             "%ld retries left.\n",
             m[retry], per->retry_sleep/1000L, per->retry_numretries);
 
-      tool_go_sleep(per->retry_sleep);
       per->retry_numretries--;
+      tool_go_sleep(sleeptime);
       if(!config->retry_delay) {
         per->retry_sleep *= 2;
         if(per->retry_sleep > RETRY_SLEEP_MAX)