Index: src/select.c
==================================================================
--- src/select.c
+++ src/select.c
@@ -5493,10 +5493,11 @@
 **    SELECT (SELECT count(*) FROM t1)+(SELECT count(*) FROM t2)
 **
 ** The transformation only works if all of the following are true:
 **
 **   *  The subquery is a UNION ALL of two or more terms
+**   *  The subquery does not have a LIMIT clause
 **   *  There is no WHERE or GROUP BY or HAVING clauses on the subqueries
 **   *  The outer query is a simple count(*)
 **
 ** Return TRUE if the optimization is undertaken.
 */
@@ -5516,10 +5517,11 @@
   if( pSub==0 ) return 0;                           /* The FROM is a subquery */
   if( pSub->pPrior==0 ) return 0;                   /* Must be a compound ry */
   do{
     if( pSub->op!=TK_ALL && pSub->pPrior ) return 0;  /* Must be UNION ALL */
     if( pSub->pWhere ) return 0;                      /* No WHERE clause */
+    if( pSub->pLimit ) return 0;                      /* No LIMIT clause */
     if( pSub->selFlags & SF_Aggregate ) return 0;     /* Not an aggregate */
     pSub = pSub->pPrior;                              /* Repeat over compound */
   }while( pSub );
 
   /* If we reach this point then it is OK to perform the transformation */
@@ -5776,10 +5778,20 @@
     }
 #endif
   }else{
     SELECTTRACE(0x100,pParse,p,("Constant propagation not helpful\n"));
   }
+
+#ifdef SQLITE_COUNTOFVIEW_OPTIMIZATION
+  if( OptimizationEnabled(db, SQLITE_QueryFlattener|SQLITE_CountOfView)
+   && countOfViewOptimization(pParse, p)
+  ){
+    if( db->mallocFailed ) goto select_end;
+    pEList = p->pEList;
+    pTabList = p->pSrc;
+  }
+#endif
 
   /* For each term in the FROM clause, do two things:
   ** (1) Authorized unreferenced tables
   ** (2) Generate code for all sub-queries
   */
@@ -5953,20 +5965,10 @@
 #if SELECTTRACE_ENABLED
   if( sqlite3SelectTrace & 0x400 ){
     SELECTTRACE(0x400,pParse,p,("After all FROM-clause analysis:\n"));
     sqlite3TreeViewSelect(0, p, 0);
   }
-#endif
-
-#ifdef SQLITE_COUNTOFVIEW_OPTIMIZATION
-  if( OptimizationEnabled(db, SQLITE_QueryFlattener|SQLITE_CountOfView)
-   && countOfViewOptimization(pParse, p)
-  ){
-    if( db->mallocFailed ) goto select_end;
-    pEList = p->pEList;
-    pTabList = p->pSrc;
-  }
 #endif
 
   /* If the query is DISTINCT with an ORDER BY but is not an aggregate, and 
   ** if the select-list is the same as the ORDER BY list, then this query
   ** can be rewritten as a GROUP BY. In other words, this:

ADDED   test/countofview.test
Index: test/countofview.test
==================================================================
--- /dev/null
+++ test/countofview.test
@@ -0,0 +1,44 @@
+# 2018-08-04
+#
+# The author disclaims copyright to this source code.  In place of
+# a legal notice, here is a blessing:
+#
+#    May you do good and not evil.
+#    May you find forgiveness for yourself and forgive others.
+#    May you share freely, never taking more than you give.
+#
+#***********************************************************************
+# 
+#
+
+set testdir [file dirname $argv0]
+source $testdir/tester.tcl
+source $testdir/malloc_common.tcl
+set testprefix countofview
+
+do_execsql_test 1.0 {
+  CREATE TABLE t2(c);
+  CREATE TABLE t3(f);
+
+  INSERT INTO t2 VALUES(1), (2);
+  INSERT INTO t3 VALUES(3);
+}
+
+do_execsql_test 1.1 {
+  select c from t2 union all select f from t3 limit 1 offset 1
+} {2}
+
+do_execsql_test 1.2 {
+  select count(*) from (
+    select c from t2 union all select f from t3 limit 1 offset 1
+  )
+} {1}
+
+do_execsql_test 1.3 {
+  select count(*) from (
+    select c from t2 union all select f from t3
+  )
+} {3}
+
+finish_test
+