Index: src/wherecode.c
==================================================================
--- src/wherecode.c
+++ src/wherecode.c
@@ -1692,10 +1692,29 @@
       VdbeCoverageIf(v, op==OP_Last);    testcase( op==OP_Last );
       VdbeCoverageIf(v, op==OP_SeekGT);  testcase( op==OP_SeekGT );
       VdbeCoverageIf(v, op==OP_SeekGE);  testcase( op==OP_SeekGE );
       VdbeCoverageIf(v, op==OP_SeekLE);  testcase( op==OP_SeekLE );
       VdbeCoverageIf(v, op==OP_SeekLT);  testcase( op==OP_SeekLT );
+
+      if( bSeekPastNull && (pLoop->wsFlags & WHERE_TOP_LIMIT)==0 ){
+        /* If bSeekPastNull is set only to skip past the NULL values for
+        ** a query like "SELECT min(a), b FROM t1", then add code so that
+        ** if there are no rows with (a IS NOT NULL), then do the seek 
+        ** without jumping past NULLs instead. This allows the code in 
+        ** select.c to pick a value for "b" in the above query.  */
+        assert( startEq==0 && (op==OP_SeekGT || op==OP_SeekLT) );
+        assert( (pWInfo->wctrlFlags&WHERE_ORDERBY_MIN)!=0 && pWInfo->nOBSat>0 );
+        sqlite3VdbeChangeP2(v, -1, sqlite3VdbeCurrentAddr(v)+1);
+        sqlite3VdbeAddOp2(v, OP_Goto, 0, sqlite3VdbeCurrentAddr(v)+2);
+
+        op = aStartOp[(start_constraints<<2) + (1<<1) + bRev];
+        assert( op!=0 );
+        sqlite3VdbeAddOp4Int(v, op, iIdxCur, addrNxt, regBase, nConstraint);
+        VdbeCoverage(v);
+        VdbeCoverageIf(v, op==OP_SeekGE);  testcase( op==OP_SeekGE );
+        VdbeCoverageIf(v, op==OP_SeekLE);  testcase( op==OP_SeekLE );
+      }
     }
 
     /* Load the value for the inequality constraint at the end of the
     ** range (if any).
     */

Index: test/minmax4.test
==================================================================
--- test/minmax4.test
+++ test/minmax4.test
@@ -17,10 +17,11 @@
 # the maximum q.
 #
 
 set testdir [file dirname $argv0]
 source $testdir/tester.tcl
+set testprefix minmax4
 
 ifcapable !compound {
   finish_test
   return
 }
@@ -146,8 +147,35 @@
   db eval {
     SELECT a, min(b), b, min(c), c FROM t2 GROUP BY a ORDER BY a;
   }
 } {1 1 {} 2 2 2 3 3 5 5}
 
-
+#-------------------------------------------------------------------------
+foreach {tn sql} {
+  1 { CREATE INDEX i1 ON t1(a) }
+  2 { CREATE INDEX i1 ON t1(a DESC) }
+  3 { }
+} {
+  reset_db
+  do_execsql_test 3.$tn.0 {
+    CREATE TABLE t1(a, b);
+    INSERT INTO t1 VALUES(NULL, 1);
+  }
+  execsql $sql
+  do_execsql_test 3.$tn.1 {
+    SELECT min(a), b FROM t1;
+  } {{} 1}
+  do_execsql_test 3.$tn.2 {
+    SELECT min(a), b FROM t1 WHERE a<50;
+  } {{} {}}
+  do_execsql_test 3.$tn.3 {
+    INSERT INTO t1 VALUES(2, 2);
+  }
+  do_execsql_test 3.$tn.4 {
+    SELECT min(a), b FROM t1;
+  } {2 2}
+  do_execsql_test 3.$tn.5 {
+    SELECT min(a), b FROM t1 WHERE a<50;
+  } {2 2}
+}
 
 finish_test