diff --git a/lib/getinfo.c b/lib/getinfo.c
index e094ffd134..a59c2d3eb2 100644
--- a/lib/getinfo.c
+++ b/lib/getinfo.c
@@ -281,7 +281,12 @@ static CURLcode getinfo_long(struct Curl_easy *data, CURLINFO info,
     *param_longp = data->state.os_errno;
     break;
   case CURLINFO_NUM_CONNECTS:
-    *param_longp = data->info.numconnects;
+#if SIZEOF_LONG < SIZEOF_CURL_OFF_T
+    if(data->info.numconnects > LONG_MAX)
+      *param_longp = LONG_MAX;
+    else
+#endif
+      *param_longp = (long)data->info.numconnects;
     break;
   case CURLINFO_LASTSOCKET:
     sockfd = Curl_getconnectinfo(data, NULL);
diff --git a/lib/progress.c b/lib/progress.c
index 9cbd2674f9..433c2b3498 100644
--- a/lib/progress.c
+++ b/lib/progress.c
@@ -152,11 +152,9 @@ UNITTEST CURLcode pgrs_speedcheck(struct Curl_easy *data,
 
         if(howlong >= data->set.low_speed_time * 1000) {
           /* too long */
-          failf(data,
-                "Operation too slow. "
-                "Less than %ld bytes/sec transferred the last %ld seconds",
-                data->set.low_speed_limit,
-                data->set.low_speed_time);
+          failf(data, "Operation too slow. Less than %" FMT_OFF_T
+                " bytes/sec transferred the last %u seconds",
+                data->set.low_speed_limit, data->set.low_speed_time);
           return CURLE_OPERATION_TIMEDOUT;
         }
       }
diff --git a/lib/rtsp.c b/lib/rtsp.c
index 93bcbeb4e8..f2bf647166 100644
--- a/lib/rtsp.c
+++ b/lib/rtsp.c
@@ -66,8 +66,8 @@ struct rtsp_conn {
 
 /* RTSP transfer data */
 struct RTSP {
-  long CSeq_sent; /* CSeq of this request */
-  long CSeq_recv; /* CSeq received */
+  uint32_t CSeq_sent; /* CSeq of this request */
+  uint32_t CSeq_recv; /* CSeq received */
 };
 
 #define RTP_PKT_LENGTH(p) ((((unsigned int)((unsigned char)((p)[2]))) << 8) | \
@@ -245,16 +245,16 @@ static CURLcode rtsp_done(struct Curl_easy *data,
 
   if(!status && !httpStatus) {
     /* Check the sequence numbers */
-    long CSeq_sent = rtsp->CSeq_sent;
-    long CSeq_recv = rtsp->CSeq_recv;
+    uint32_t CSeq_sent = rtsp->CSeq_sent;
+    uint32_t CSeq_recv = rtsp->CSeq_recv;
     if((data->set.rtspreq != RTSPREQ_RECEIVE) && (CSeq_sent != CSeq_recv)) {
       failf(data,
-            "The CSeq of this request %ld did not match the response %ld",
+            "The CSeq of this request %u did not match the response %u",
             CSeq_sent, CSeq_recv);
       return CURLE_RTSP_CSEQ_ERROR;
     }
     if(data->set.rtspreq == RTSPREQ_RECEIVE && (rtspc->rtp_channel == -1)) {
-      infof(data, "Got an RTP Receive with a CSeq of %ld", CSeq_recv);
+      infof(data, "Got an RTP Receive with a CSeq of %u", CSeq_recv);
     }
     if(data->set.rtspreq == RTSPREQ_RECEIVE &&
        data->req.eos_written) {
@@ -346,11 +346,11 @@ static CURLcode rtsp_do(struct Curl_easy *data, bool *done)
 {
   struct connectdata *conn = data->conn;
   CURLcode result = CURLE_OK;
-  Curl_RtspReq rtspreq = data->set.rtspreq;
+  const Curl_RtspReq rtspreq = data->set.rtspreq;
   struct RTSP *rtsp = Curl_meta_get(data, CURL_META_RTSP_EASY);
   struct dynbuf req_buffer;
-  unsigned char httpversion = 11; /* RTSP is close to HTTP/1.1, sort of... */
-
+  const unsigned char httpversion = 11; /* RTSP is close to HTTP/1.1, sort
+                                           of... */
   const char *p_request = NULL;
   const char *p_session_id = NULL;
   const char *p_accept = NULL;
@@ -573,7 +573,7 @@ static CURLcode rtsp_do(struct Curl_easy *data, bool *done)
   result =
     curlx_dyn_addf(&req_buffer,
                    "%s %s RTSP/1.0\r\n" /* Request Stream-URI RTSP/1.0 */
-                   "CSeq: %ld\r\n", /* CSeq */
+                   "CSeq: %u\r\n", /* CSeq */
                    p_request, p_stream_uri, rtsp->CSeq_sent);
   if(result)
     goto out;
@@ -995,12 +995,11 @@ CURLcode Curl_rtsp_parseheader(struct Curl_easy *data, const char *header)
     if(!rtsp)
       return CURLE_FAILED_INIT;
     curlx_str_passblanks(&p);
-    if(curlx_str_number(&p, &CSeq, LONG_MAX)) {
+    if(curlx_str_number(&p, &CSeq, UINT_MAX)) {
       failf(data, "Unable to read the CSeq header: [%s]", header);
       return CURLE_RTSP_CSEQ_ERROR;
     }
-    rtsp->CSeq_recv = (long)CSeq; /* mark the request */
-    data->state.rtsp_CSeq_recv = (long)CSeq; /* update the handle */
+    data->state.rtsp_CSeq_recv = rtsp->CSeq_recv = (uint32_t)CSeq;
   }
   else if(checkprefix("Session:", header)) {
     const char *start, *end;
diff --git a/lib/setopt.c b/lib/setopt.c
index 4b66cf3345..402a1f6d9a 100644
--- a/lib/setopt.c
+++ b/lib/setopt.c
@@ -1050,9 +1050,10 @@ static CURLcode setopt_long(struct Curl_easy *data, CURLoption option,
     s->low_speed_limit = arg;
     break;
   case CURLOPT_LOW_SPEED_TIME:
-    if(arg < 0)
-      return CURLE_BAD_FUNCTION_ARGUMENT;
-    s->low_speed_time = arg;
+    result = value_range(&arg, 0, 0, USHRT_MAX);
+    if(result)
+      return result;
+    s->low_speed_time = (uint16_t)arg;
     break;
   case CURLOPT_PORT:
     if((arg < 0) || (arg > 65535))
@@ -1190,11 +1191,17 @@ static CURLcode setopt_long(struct Curl_easy *data, CURLoption option,
   case CURLOPT_RTSP_REQUEST:
     return setopt_RTSP_REQUEST(data, arg);
   case CURLOPT_RTSP_CLIENT_CSEQ:
-    data->state.rtsp_next_client_CSeq = arg;
+    result = value_range(&arg, 0, 0, INT_MAX);
+    if(result)
+      return result;
+    data->state.rtsp_next_client_CSeq = (uint32_t)arg;
     break;
 
   case CURLOPT_RTSP_SERVER_CSEQ:
-    data->state.rtsp_next_server_CSeq = arg;
+    result = value_range(&arg, 0, 0, INT_MAX);
+    if(result)
+      return result;
+    data->state.rtsp_next_server_CSeq = (uint32_t)arg;
     break;
 
 #endif /* !CURL_DISABLE_RTSP */
@@ -1231,9 +1238,7 @@ static CURLcode setopt_long(struct Curl_easy *data, CURLoption option,
     return setopt_set_timeout_ms(&s->happy_eyeballs_timeout, arg);
 
   case CURLOPT_UPKEEP_INTERVAL_MS:
-    if(arg < 0)
-      return CURLE_BAD_FUNCTION_ARGUMENT;
-    s->upkeep_interval_ms = arg;
+    return setopt_set_timeout_ms(&s->upkeep_interval_ms, arg);
     break;
   case CURLOPT_MAXAGE_CONN:
     return setopt_set_timeout_sec(&s->conn_max_idle_ms, arg);
diff --git a/lib/urldata.h b/lib/urldata.h
index bc932d2e40..84bfaeb102 100644
--- a/lib/urldata.h
+++ b/lib/urldata.h
@@ -753,11 +753,11 @@ struct PureInfo {
   time_t filetime; /* If requested, this is might get set. Set to -1 if the
                       time was unretrievable. */
   curl_off_t request_size; /* the amount of bytes sent in the request(s) */
+  curl_off_t numconnects; /* how many new connections libcurl created */
   uint32_t proxyauthavail; /* what proxy auth types were announced */
   uint32_t httpauthavail;  /* what host auth types were announced */
   uint32_t proxyauthpicked; /* selected proxy auth type */
   uint32_t httpauthpicked;  /* selected host auth type */
-  long numconnects; /* how many new connection did libcurl created */
   char *contenttype; /* the content type of the object */
   char *wouldredirect; /* URL this would have been redirected to if asked to */
   curl_off_t retry_after; /* info from Retry-After: header */
@@ -998,10 +998,9 @@ struct UrlState {
 
 #ifndef CURL_DISABLE_RTSP
   /* This RTSP state information survives requests and connections */
-  long rtsp_next_client_CSeq; /* the session's next client CSeq */
-  long rtsp_next_server_CSeq; /* the session's next server CSeq */
-  long rtsp_CSeq_recv; /* most recent CSeq received */
-
+  uint32_t rtsp_next_client_CSeq; /* the session's next client CSeq */
+  uint32_t rtsp_next_server_CSeq; /* the session's next server CSeq */
+  uint32_t rtsp_CSeq_recv; /* most recent CSeq received */
   uint8_t rtp_channel_mask[32]; /* for the correctness checking of the
                                          interleaved data */
 #endif
@@ -1334,8 +1333,7 @@ struct UserDefined {
   timediff_t conn_max_age_ms; /* max time since creation to allow a
                                  connection that is to be reused */
   curl_off_t filesize;  /* size of file to upload, -1 means unknown */
-  long low_speed_limit; /* bytes/second */
-  long low_speed_time;  /* number of seconds */
+  curl_off_t low_speed_limit; /* bytes/second */
   curl_off_t max_send_speed; /* high speed limit in bytes/second for upload */
   curl_off_t max_recv_speed; /* high speed limit in bytes/second for
                                 download */
@@ -1433,7 +1431,8 @@ struct UserDefined {
   curl_resolver_start_callback resolver_start; /* optional callback called
                                                   before resolver start */
   void *resolver_start_client; /* pointer to pass to resolver start callback */
-  long upkeep_interval_ms;      /* Time between calls for connection upkeep. */
+  timediff_t upkeep_interval_ms; /* Time between calls for connection
+                                    upkeep. */
   CURLU *uh; /* URL handle for the current parsed URL */
 #ifndef CURL_DISABLE_HTTP
   void *trailer_data; /* pointer to pass to trailer data callback */
@@ -1450,6 +1449,7 @@ struct UserDefined {
                          set to -1 for infinity */
   uint16_t expect_100_timeout; /* in milliseconds */
   uint16_t use_port; /* which port to use (when not using default) */
+  uint16_t low_speed_time;  /* number of seconds */
 #ifndef CURL_DISABLE_BINDLOCAL
   uint16_t localport; /* local port number to bind to */
   uint16_t localportrange; /* number of additional port numbers to test