Index: src/insert.c
==================================================================
--- src/insert.c
+++ src/insert.c
@@ -1547,16 +1547,29 @@
       onError = overrideError;
     }else if( onError==OE_Default ){
       onError = OE_Abort;
     }
 
-    if( ix==0 && pPk==pIdx && onError==OE_Replace && pPk->pNext==0 ){
+    /* Collision detection may be omitted if all of the following are true:
+    **   (1) The conflict resolution algorithm is REPLACE
+    **   (2) The table is a WITHOUT ROWID table
+    **   (3) There are no secondary indexes on the table
+    **   (4) No delete triggers need to be fired if there is a conflict
+    **   (5) No FK constraint counters need to be updated if a conflict occurs.
+    */ 
+    if( (ix==0 && pIdx->pNext==0)                   /* Condition 3 */
+     && pPk==pIdx                                   /* Condition 2 */
+     && onError==OE_Replace                         /* Condition 1 */
+     && ( 0==(db->flags&SQLITE_RecTriggers) ||      /* Condition 4 */
+          0==sqlite3TriggersExist(pParse, pTab, TK_DELETE, 0, 0))
+     && ( 0==(db->flags&SQLITE_ForeignKeys) ||      /* Condition 5 */
+         (0==pTab->pFKey && 0==sqlite3FkReferences(pTab)))
+    ){
       sqlite3VdbeResolveLabel(v, addrUniqueOk);
       continue;
     }
 
-    
     /* Check to see if the new index entry will be unique */
     sqlite3VdbeAddOp4Int(v, OP_NoConflict, iThisCur, addrUniqueOk,
                          regIdx, pIdx->nKeyCol); VdbeCoverage(v);
 
     /* Generate code to handle collisions */

Index: test/fkey8.test
==================================================================
--- test/fkey8.test
+++ test/fkey8.test
@@ -99,7 +99,69 @@
     sqlite3_finalize $stmt
     set ret
   } $use_stmt
 }
 
+#-------------------------------------------------------------------------
+# The following tests check that foreign key constaint counters are
+# correctly updated for any implicit DELETE operations that occur
+# when a REPLACE command is executed against a WITHOUT ROWID table
+# that has no triggers or auxiliary indexes.
+#
+reset_db
+do_execsql_test 2.1.0 {
+  PRAGMA foreign_keys = on;
+  CREATE TABLE p1(a PRIMARY KEY, b) WITHOUT ROWID;
+  CREATE TABLE c1(x REFERENCES p1 DEFERRABLE INITIALLY DEFERRED);
+
+  INSERT INTO p1 VALUES(1, 'one');
+  INSERT INTO p1 VALUES(2, 'two');
+  INSERT INTO c1 VALUES(1);
+  INSERT INTO c1 VALUES(2);
+}
+
+do_catchsql_test 2.1.2 {
+  BEGIN;
+    DELETE FROM p1 WHERE a=1;
+    INSERT OR REPLACE INTO p1 VALUES(2, 'two');
+  COMMIT;
+} {1 {FOREIGN KEY constraint failed}}
+
+reset_db
+do_execsql_test 2.2.0 {
+  PRAGMA foreign_keys = on;
+  CREATE TABLE p2(a PRIMARY KEY, b);
+  CREATE TABLE c2(
+    x PRIMARY KEY,
+    y REFERENCES p2 DEFERRABLE INITIALLY DEFERRED
+  ) WITHOUT ROWID;
+}
+
+do_catchsql_test 2.2.1 {
+  BEGIN;
+    INSERT INTO c2 VALUES(13, 13);
+    INSERT OR REPLACE INTO c2 VALUES(13, 13);
+    DELETE FROM c2;
+  COMMIT;
+} {0 {}}
+
+reset_db
+do_execsql_test 2.3.0 {
+  PRAGMA foreign_keys = on;
+  CREATE TABLE p3(a PRIMARY KEY, b) WITHOUT ROWID;
+  CREATE TABLE c3(x REFERENCES p3);
+
+  INSERT INTO p3 VALUES(1, 'one');
+  INSERT INTO p3 VALUES(2, 'two');
+  INSERT INTO c3 VALUES(1);
+  INSERT INTO c3 VALUES(2);
+
+  CREATE TRIGGER p3d AFTER DELETE ON p3 WHEN old.a=1 BEGIN
+    INSERT OR REPLACE INTO p3 VALUES(2, 'three');
+  END;
+}
+
+do_catchsql_test 2.3.1 {
+  DELETE FROM p3 WHERE a=1
+} {1 {FOREIGN KEY constraint failed}}
 
 finish_test

ADDED   test/triggerF.test
Index: test/triggerF.test
==================================================================
--- /dev/null
+++ test/triggerF.test
@@ -0,0 +1,72 @@
+# 2017 January 4
+#
+# 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 $testdir/tester.tcl
+set testprefix triggerF
+ifcapable {!trigger} {
+  finish_test
+  return
+}
+
+
+foreach {tn sql log} {
+  1 { } { }
+
+  2 { 
+    CREATE TRIGGER trd AFTER DELETE ON t1 BEGIN
+      INSERT INTO log VALUES(old.a || old.b || (SELECT count(*) FROM t1));
+    END;
+  } {1one2 2two1 3three1}
+
+  3 { 
+    CREATE TRIGGER trd BEFORE DELETE ON t1 BEGIN
+      INSERT INTO log VALUES(old.a || old.b || (SELECT count(*) FROM t1));
+    END;
+  } {1one3 2two2 3three2}
+
+  4 { 
+    CREATE TRIGGER tr1 AFTER DELETE ON t1 BEGIN
+      INSERT INTO log VALUES(old.a || old.b || (SELECT count(*) FROM t1));
+    END;
+    CREATE TRIGGER tr2 BEFORE DELETE ON t1 BEGIN
+      INSERT INTO log VALUES(old.a || old.b || (SELECT count(*) FROM t1));
+    END;
+  } {1one3 1one2 2two2 2two1 3three2 3three1}
+
+} {
+  reset_db
+  do_execsql_test 1.$tn.0 {
+    PRAGMA recursive_triggers = on;
+    CREATE TABLE t1(a INT PRIMARY KEY, b) WITHOUT ROWID;
+    CREATE TABLE log(t);
+  }
+  
+  execsql $sql
+
+  do_execsql_test 1.$tn.1 {
+    INSERT INTO t1 VALUES(1, 'one');
+    INSERT INTO t1 VALUES(2, 'two');
+    INSERT INTO t1 VALUES(3, 'three');
+
+    DELETE FROM t1 WHERE a=1;
+    INSERT OR REPLACE INTO t1 VALUES(2, 'three');
+    UPDATE OR REPLACE t1 SET a=3 WHERE a=2;
+  }
+
+  do_execsql_test 1.$tn.2 {
+    SELECT * FROM log ORDER BY rowid;
+  } $log
+}
+
+finish_test
+