Index: ext/session/session1.test
==================================================================
--- ext/session/session1.test
+++ ext/session/session1.test
@@ -579,7 +579,26 @@
 }
 do_iterator_test 11.2 * {
   UPDATE t1 SET b = 0.0;
 } {
 }
+
+reset_db
+do_execsql_test 12.1 {
+  CREATE TABLE t1(r INTEGER PRIMARY KEY, a, b);
+  CREATE INDEX i1 ON t1(a);
+  INSERT INTO t1 VALUES(1, 1, 1);
+  INSERT INTO t1 VALUES(2, 1, 2);
+  INSERT INTO t1 VALUES(3, 1, 3);
+}
+
+do_iterator_test 12.2 * {
+  UPDATE t1 SET b='one' WHERE a=1;
+} {
+  {UPDATE t1 0 X.. {i 1 {} {} i 1} {{} {} {} {} t one}}
+  {UPDATE t1 0 X.. {i 2 {} {} i 2} {{} {} {} {} t one}}
+  {UPDATE t1 0 X.. {i 3 {} {} i 3} {{} {} {} {} t one}}
+}
+
+
 
 finish_test

Index: src/sqliteInt.h
==================================================================
--- src/sqliteInt.h
+++ src/sqliteInt.h
@@ -2590,11 +2590,11 @@
 #define WHERE_DISTINCTBY       0x0080 /* pOrderby is really a DISTINCT clause */
 #define WHERE_WANT_DISTINCT    0x0100 /* All output needs to be distinct */
 #define WHERE_SORTBYGROUP      0x0200 /* Support sqlite3WhereIsSorted() */
 #define WHERE_SEEK_TABLE       0x0400 /* Do not defer seeks on main table */
 #define WHERE_ORDERBY_LIMIT    0x0800 /* ORDERBY+LIMIT on the inner loop */
-                        /*     0x1000    not currently used */
+#define WHERE_SEEK_UNIQ_TABLE  0x1000 /* Do not defer seeks if unique */
                         /*     0x2000    not currently used */
 #define WHERE_USE_LIMIT        0x4000 /* Use the LIMIT in cost estimates */
                         /*     0x8000    not currently used */
 
 /* Allowed return values from sqlite3WhereIsDistinct()

Index: src/update.c
==================================================================
--- src/update.c
+++ src/update.c
@@ -390,11 +390,11 @@
   ** Do not consider a single-pass strategy for a multi-row update if
   ** there are any triggers or foreign keys to process, or rows may
   ** be deleted as a result of REPLACE conflict handling. Any of these
   ** things might disturb a cursor being used to scan through the table
   ** or index, causing a single-pass approach to malfunction.  */
-  flags = WHERE_ONEPASS_DESIRED | WHERE_SEEK_TABLE;
+  flags = WHERE_ONEPASS_DESIRED|WHERE_SEEK_UNIQ_TABLE;
   if( !pParse->nested && !pTrigger && !hasFK && !chngKey && !bReplace ){
     flags |= WHERE_ONEPASS_MULTIROW;
   }
   pWInfo = sqlite3WhereBegin(pParse, pTabList, pWhere, 0, 0, flags, iIdxCur);
   if( pWInfo==0 ) goto update_cleanup;

Index: src/wherecode.c
==================================================================
--- src/wherecode.c
+++ src/wherecode.c
@@ -1589,11 +1589,14 @@
 
     /* Seek the table cursor, if required */
     if( omitTable ){
       /* pIdx is a covering index.  No need to access the main table. */
     }else if( HasRowid(pIdx->pTable) ){
-      if( (pWInfo->wctrlFlags & WHERE_SEEK_TABLE)!=0 ){
+      if( (pWInfo->wctrlFlags & WHERE_SEEK_TABLE) || (
+          (pWInfo->wctrlFlags & WHERE_SEEK_UNIQ_TABLE) 
+       && (pWInfo->eOnePass==ONEPASS_SINGLE)
+      )){
         iRowidReg = ++pParse->nMem;
         sqlite3VdbeAddOp2(v, OP_IdxRowid, iIdxCur, iRowidReg);
         sqlite3ExprCacheStore(pParse, iCur, -1, iRowidReg);
         sqlite3VdbeAddOp3(v, OP_NotExists, iCur, 0, iRowidReg);
         VdbeCoverage(v);

Index: test/update2.test
==================================================================
--- test/update2.test
+++ test/update2.test
@@ -173,8 +173,33 @@
     5 a 15 5
     6 a 16 6
     7 a 17 7
   }
 }
+
+#-------------------------------------------------------------------------
+#
+do_execsql_test 5.0 {
+  CREATE TABLE x1(a INTEGER PRIMARY KEY, b, c);
+  CREATE INDEX x1c ON x1(b, c);
+  INSERT INTO x1 VALUES(1, 'a', 1);
+  INSERT INTO x1 VALUES(2, 'a', 2);
+  INSERT INTO x1 VALUES(3, 'a', 3);
+}
+
+do_execsql_test 5.1.1 {
+  UPDATE x1 SET c=c+1 WHERE b='a';
+}
+
+do_execsql_test 5.1.2 {
+  SELECT * FROM x1;
+} {1 a 2 2 a 3 3 a 4}
+
+do_test 5.2 {
+  catch { array unset A }
+  db eval { EXPLAIN UPDATE x1 SET c=c+1 WHERE b='a' } { incr A($opcode) }
+  set A(NotExists)
+} {1}
+
 
 finish_test