Index: src/where.c
==================================================================
--- src/where.c
+++ src/where.c
@@ -1883,20 +1883,19 @@
 
 /*
 ** Return TRUE if all of the following are true:
 **
 **   (1)  X has the same or lower cost that Y
-**   (2)  X is a proper subset of Y
-**   (3)  X skips at least as many columns as Y
+**   (2)  X users fewer WHERE clause terms than Y
+**   (3)  Every WHERE clause term used by X is also used by Y
+**   (4)  X skips at least as many columns as Y
+**   (5)  If X is a covering index, than Y is too
 **
-** By "proper subset" we mean that X uses fewer WHERE clause terms
-** than Y and that every WHERE clause term used by X is also used
-** by Y.
-**
+** Conditions (2) and (3) mean that X is a "proper subset" of Y.
 ** If X is a proper subset of Y then Y is a better choice and ought
 ** to have a lower cost.  This routine returns TRUE when that cost 
-** relationship is inverted and needs to be adjusted.  The third rule
+** relationship is inverted and needs to be adjusted.  Constraint (4)
 ** was added because if X uses skip-scan less than Y it still might
 ** deserve a lower cost even if it is a proper subset of Y.
 */
 static int whereLoopCheaperProperSubset(
   const WhereLoop *pX,       /* First WhereLoop to compare */
@@ -1915,10 +1914,14 @@
     if( pX->aLTerm[i]==0 ) continue;
     for(j=pY->nLTerm-1; j>=0; j--){
       if( pY->aLTerm[j]==pX->aLTerm[i] ) break;
     }
     if( j<0 ) return 0;  /* X not a subset of Y since term X[i] not used by Y */
+  }
+  if( (pX->wsFlags&WHERE_IDX_ONLY)!=0 
+   && (pY->wsFlags&WHERE_IDX_ONLY)==0 ){
+    return 0;  /* Constraint (5) */
   }
   return 1;  /* All conditions meet */
 }
 
 /*

Index: test/analyze9.test
==================================================================
--- test/analyze9.test
+++ test/analyze9.test
@@ -1050,12 +1050,15 @@
 } {}
 
 do_eqp_test 23.1 {
   SELECT * FROM t4 WHERE 
     (e=1 AND b='xyz' AND c='zyx' AND a<'AEA') AND f<300
+  -- Formerly used index i41.  But i41 is not a covering index whereas
+  -- the PRIMARY KEY is a covering index, and so as of 2017-10-15, the
+  -- PRIMARY KEY is preferred.
 } {
-  0 0 0 {SEARCH TABLE t4 USING INDEX i41 (e=? AND c=? AND b=? AND a<?)}
+  0 0 0 {SEARCH TABLE t4 USING PRIMARY KEY (c=? AND b=? AND a<?)}
 }
 do_eqp_test 23.2 {
   SELECT * FROM t4 WHERE 
     (e=1 AND b='xyz' AND c='zyx' AND a<'JJJ') AND f<300
 } {