Index: src/update.c
==================================================================
--- src/update.c
+++ src/update.c
@@ -126,10 +126,11 @@
   Trigger *pTrigger;     /* List of triggers on pTab, if required */
   int tmask;             /* Mask of TRIGGER_BEFORE|TRIGGER_AFTER */
 #endif
   int newmask;           /* Mask of NEW.* columns accessed by BEFORE triggers */
   int iEph = 0;          /* Ephemeral table holding all primary key values */
+  int nKey;              /* Number of elements in regKey */
 
   /* Register Allocations */
   int regRowCount = 0;   /* A count of rows changed */
   int regOldRowid;       /* The old rowid */
   int regNewRowid;       /* The new rowid */
@@ -351,30 +352,40 @@
     */
     sqlite3WhereEnd(pWInfo);
   }else{
     int iPk;         /* First of nPk memory cells holding PRIMARY KEY value */
     i16 nPk;         /* Number of components of the PRIMARY KEY */
+    int addrOpen;    /* Address of the OpenEphemeral instruction */
 
     assert( pPk!=0 );
     nPk = pPk->nKeyCol;
     iPk = pParse->nMem+1;
     pParse->nMem += nPk;
     regKey = ++pParse->nMem;
     iEph = pParse->nTab++;
-    sqlite3VdbeAddOp2(v, OP_OpenEphemeral, iEph, nPk);
+    sqlite3VdbeAddOp2(v, OP_Null, 0, iPk);
+    addrOpen = sqlite3VdbeAddOp2(v, OP_OpenEphemeral, iEph, nPk);
     sqlite3VdbeSetP4KeyInfo(pParse, pPk);
-    pWInfo = sqlite3WhereBegin(pParse, pTabList, pWhere, 0, 0, 0, 0);
+    pWInfo = sqlite3WhereBegin(pParse, pTabList, pWhere, 0, 0, 
+                               WHERE_ONEPASS_DESIRED, 0);
     if( pWInfo==0 ) goto update_cleanup;
+    okOnePass = sqlite3WhereOkOnePass(pWInfo);
     for(i=0; i<nPk; i++){
       sqlite3ExprCodeGetColumnOfTable(v, pTab, iDataCur, pPk->aiColumn[i],
                                       iPk+i);
     }
-    sqlite3VdbeAddOp4(v, OP_MakeRecord, iPk, nPk, regKey,
-                      sqlite3IndexAffinityStr(v, pPk), P4_TRANSIENT);
-    sqlite3VdbeAddOp2(v, OP_IdxInsert, iEph, regKey);
+    if( okOnePass ){
+      sqlite3VdbeChangeToNoop(v, addrOpen);
+      nKey = nPk;
+      regKey = iPk;
+    }else{
+      sqlite3VdbeAddOp4(v, OP_MakeRecord, iPk, nPk, regKey,
+                        sqlite3IndexAffinityStr(v, pPk), P4_TRANSIENT);
+      sqlite3VdbeAddOp2(v, OP_IdxInsert, iEph, regKey);
+      nKey = 0;
+    }
     sqlite3WhereEnd(pWInfo);
-    okOnePass = 0;
   }
 
   /* Initialize the count of updated rows
   */
   if( (db->flags & SQLITE_CountRows) && !pParse->pTriggerTab ){
@@ -415,18 +426,21 @@
     }
   }
 
   /* Top of the update loop */
   labelBreak = sqlite3VdbeMakeLabel(v);
-  if( pPk ){
+  if( okOnePass ){
+    labelContinue = labelBreak;
+    sqlite3VdbeAddOp2(v, OP_IsNull, pPk ? regKey : regOldRowid, labelBreak);
+    if( pPk ){
+      sqlite3VdbeAddOp4Int(v, OP_NotFound, iDataCur, labelBreak, regKey, nKey);
+    }
+  }else if( pPk ){
     labelContinue = sqlite3VdbeMakeLabel(v);
     sqlite3VdbeAddOp2(v, OP_Rewind, iEph, labelBreak);
     addrTop = sqlite3VdbeAddOp2(v, OP_RowKey, iEph, regKey);
     sqlite3VdbeAddOp4Int(v, OP_NotFound, iDataCur, labelContinue, regKey, 0);
-  }else if( okOnePass ){
-    labelContinue = labelBreak;
-    sqlite3VdbeAddOp2(v, OP_IsNull, regOldRowid, labelBreak);
   }else{
     labelContinue = sqlite3VdbeAddOp3(v, OP_RowSetRead, regRowSet, labelBreak,
                              regOldRowid);
     sqlite3VdbeAddOp3(v, OP_NotExists, iDataCur, labelContinue, regOldRowid);
   }
@@ -514,11 +528,11 @@
     ** required. This behavior - what happens when the row being updated
     ** is deleted or renamed by a BEFORE trigger - is left undefined in the
     ** documentation.
     */
     if( pPk ){
-      sqlite3VdbeAddOp4Int(v, OP_NotFound, iDataCur, labelContinue, regKey, 0);
+      sqlite3VdbeAddOp4Int(v, OP_NotFound, iDataCur, labelContinue,regKey,nKey);
     }else{
       sqlite3VdbeAddOp3(v, OP_NotExists, iDataCur, labelContinue, regOldRowid);
     }
 
     /* If it did not delete it, the row-trigger may still have modified 
@@ -546,11 +560,11 @@
       sqlite3FkCheck(pParse, pTab, regOldRowid, 0, aXRef, chngKey);
     }
 
     /* Delete the index entries associated with the current record.  */
     if( pPk ){
-      j1 = sqlite3VdbeAddOp4Int(v, OP_NotFound, iDataCur, 0, regKey, 0);
+      j1 = sqlite3VdbeAddOp4Int(v, OP_NotFound, iDataCur, 0, regKey, nKey);
     }else{
       j1 = sqlite3VdbeAddOp3(v, OP_NotExists, iDataCur, 0, regOldRowid);
     }
     sqlite3GenerateRowIndexDelete(pParse, pTab, iDataCur, iIdxCur, aRegIdx);
   
@@ -590,14 +604,16 @@
       TRIGGER_AFTER, pTab, regOldRowid, onError, labelContinue);
 
   /* Repeat the above with the next record to be updated, until
   ** all record selected by the WHERE clause have been updated.
   */
-  if( pPk ){
+  if( okOnePass ){
+    /* Nothing to do at end-of-loop for a single-pass */
+  }else if( pPk ){
     sqlite3VdbeResolveLabel(v, labelContinue);
     sqlite3VdbeAddOp2(v, OP_Next, iEph, addrTop);
-  }else if( !okOnePass ){
+  }else{
     sqlite3VdbeAddOp2(v, OP_Goto, 0, labelContinue);
   }
   sqlite3VdbeResolveLabel(v, labelBreak);
 
   /* Close all tables */

Index: src/where.c
==================================================================
--- src/where.c
+++ src/where.c
@@ -4637,13 +4637,14 @@
         pNew->wsFlags = (m==0) ? (WHERE_IDX_ONLY|WHERE_INDEXED) : WHERE_INDEXED;
       }
 
       /* Full scan via index */
       if( b
+       || !HasRowid(pTab)
        || ( m==0
          && pProbe->bUnordered==0
-         && (!HasRowid(pTab) || pProbe->szIdxRow<pTab->szTabRow)
+         && (pProbe->szIdxRow<pTab->szTabRow)
          && (pWInfo->wctrlFlags & WHERE_ONEPASS_DESIRED)==0
          && sqlite3GlobalConfig.bUseCis
          && OptimizationEnabled(pWInfo->pParse->db, SQLITE_CoverIdxScan)
           )
       ){
@@ -4655,11 +4656,10 @@
           **     is smaller for smaller indices, thus favoring them.
           */
           pNew->rRun = sqlite3LogEstAdd(rSize,rLogSize) + 1 +
                         (15*pProbe->szIdxRow)/pTab->szTabRow;
         }else{
-          assert( b!=0 ); 
           /* TUNING: Cost of scanning a non-covering index is (N+1)*log2(N)
           ** which we will simplify to just N*log2(N) */
           pNew->rRun = rSize + rLogSize;
         }
         whereLoopOutputAdjust(pWC, pNew);
@@ -5988,11 +5988,13 @@
   */
   assert( (wctrlFlags & WHERE_ONEPASS_DESIRED)==0 || pWInfo->nLevel==1 );
   if( (wctrlFlags & WHERE_ONEPASS_DESIRED)!=0 
    && (pWInfo->a[0].pWLoop->wsFlags & WHERE_ONEROW)!=0 ){
     pWInfo->okOnePass = 1;
-    pWInfo->a[0].pWLoop->wsFlags &= ~WHERE_IDX_ONLY;
+    if( HasRowid(pTabList->a[0].pTab) ){
+      pWInfo->a[0].pWLoop->wsFlags &= ~WHERE_IDX_ONLY;
+    }
   }
 
   /* Open all tables in the pTabList and any indices selected for
   ** searching those tables.
   */