diff --git a/lib/multi.c b/lib/multi.c
index 32bd8bfd1..aa8eaf06b 100644
--- a/lib/multi.c
+++ b/lib/multi.c
@@ -307,6 +307,14 @@ struct Curl_multi *Curl_multi_handle(int hashsize, /* socket hash */
   if(!multi->msglist)
     goto error;
 
+  /* allocate a new easy handle to use when closing cached connections */
+  multi->closure_handle = curl_easy_init();
+  if(!multi->closure_handle)
+    goto error;
+
+  multi->closure_handle->multi = multi;
+  multi->closure_handle->state.conn_cache = multi->conn_cache;
+
   multi->max_pipeline_length = 5;
   return (CURLM *) multi;
 
@@ -318,6 +326,8 @@ struct Curl_multi *Curl_multi_handle(int hashsize, /* socket hash */
   multi->hostcache = NULL;
   Curl_conncache_destroy(multi->conn_cache);
   multi->conn_cache = NULL;
+  Curl_close(multi->closure_handle);
+  multi->closure_handle = NULL;
 
   free(multi);
   return NULL;
@@ -329,22 +339,12 @@ CURLM *curl_multi_init(void)
                            CURL_CONNECTION_HASH_SIZE);
 }
 
-/*
- * Store a pointed to the multi handle within the easy handle's data struct.
- */
-static void easy_addmulti(struct SessionHandle *data,
-                          void *multi)
-{
-  data->multi = multi;
-}
-
 CURLMcode curl_multi_add_handle(CURLM *multi_handle,
                                 CURL *easy_handle)
 {
   struct curl_llist *timeoutlist;
   struct Curl_multi *multi = (struct Curl_multi *)multi_handle;
   struct SessionHandle *data = (struct SessionHandle *)easy_handle;
-  struct SessionHandle *new_closure = NULL;
 
   /* First, make some basic checks that the CURLM handle is a good handle */
   if(!GOOD_MULTI_HANDLE(multi))
@@ -365,31 +365,12 @@ CURLMcode curl_multi_add_handle(CURLM *multi_handle,
   if(!timeoutlist)
     return CURLM_OUT_OF_MEMORY;
 
-  /* In case multi handle has no closure_handle yet, allocate
-     a new easy handle to use when closing cached connections */
-  if(!multi->closure_handle) {
-    new_closure = (struct SessionHandle *)curl_easy_init();
-    if(!new_closure) {
-      free(data);
-      Curl_llist_destroy(timeoutlist, NULL);
-      return CURLM_OUT_OF_MEMORY;
-    }
-  }
-
   /*
-  ** No failure allowed in this function beyond this point. And
-  ** no modification of easy nor multi handle allowed before this
-  ** except for potential multi's connection cache growing which
-  ** won't be undone in this function no matter what.
-  */
-
-  /* In case a new closure handle has been initialized above, it
-     is associated now with the multi handle which lacked one. */
-  if(new_closure) {
-    multi->closure_handle = new_closure;
-    easy_addmulti(multi->closure_handle, multi_handle);
-    multi->closure_handle->state.conn_cache = multi->conn_cache;
-  }
+   * No failure allowed in this function beyond this point. And no
+   * modification of easy nor multi handle allowed before this except for
+   * potential multi's connection cache growing which won't be undone in this
+   * function no matter what.
+   */
 
   /* Make easy handle use timeout list initialized above */
   data->state.timeoutlist = timeoutlist;
@@ -440,7 +421,7 @@ CURLMcode curl_multi_add_handle(CURLM *multi_handle,
   }
 
   /* make the SessionHandle refer back to this multi handle */
-  easy_addmulti(easy_handle, multi_handle);
+  data->multi = multi_handle;
 
   /* Set the timeout for this handle to expire really soon so that it will
      be taken care of even when this handle is added in the midst of operation
@@ -581,8 +562,7 @@ CURLMcode curl_multi_remove_handle(CURLM *multi_handle,
       data->easy_conn = NULL;
     }
 
-    easy_addmulti(data, NULL); /* clear the association to this multi
-                                  handle */
+    data->multi = NULL; /* clear the association to this multi handle */
 
     {
       /* make sure there's no pending message in the queue sent from this easy
@@ -1836,8 +1816,7 @@ CURLMcode curl_multi_cleanup(CURLM *multi_handle)
 
       /* Clear the pointer to the connection cache */
       data->state.conn_cache = NULL;
-
-      easy_addmulti(data, NULL); /* clear the association */
+      data->multi = NULL; /* clear the association */
 
       data = nextdata;
     }