diff --git a/src/backend/utils/adt/selfuncs.c b/src/backend/utils/adt/selfuncs.c
index c2aeb4b947..81602674fd 100644
--- a/src/backend/utils/adt/selfuncs.c
+++ b/src/backend/utils/adt/selfuncs.c
@@ -5494,15 +5494,35 @@ get_variable_range(PlannerInfo *root, VariableStatData *vardata,
 	/*
 	 * If we have most-common-values info, look for extreme MCVs.  This is
 	 * needed even if we also have a histogram, since the histogram excludes
-	 * the MCVs.
+	 * the MCVs.  However, if we *only* have MCVs and no histogram, we should
+	 * be pretty wary of deciding that that is a full representation of the
+	 * data.  Proceed only if the MCVs represent the whole table (to within
+	 * roundoff error).
 	 */
 	if (get_attstatsslot(&sslot, vardata->statsTuple,
 						 STATISTIC_KIND_MCV, InvalidOid,
-						 ATTSTATSSLOT_VALUES))
+						 have_data ? ATTSTATSSLOT_VALUES :
+						 (ATTSTATSSLOT_VALUES | ATTSTATSSLOT_NUMBERS)))
 	{
-		get_stats_slot_range(&sslot, opfuncoid, &opproc,
-							 collation, typLen, typByVal,
-							 &tmin, &tmax, &have_data);
+		bool		use_mcvs = have_data;
+
+		if (!have_data)
+		{
+			double		sumcommon = 0.0;
+			double		nullfrac;
+			int			i;
+
+			for (i = 0; i < sslot.nnumbers; i++)
+				sumcommon += sslot.numbers[i];
+			nullfrac = ((Form_pg_statistic) GETSTRUCT(vardata->statsTuple))->stanullfrac;
+			if (sumcommon + nullfrac > 0.99999)
+				use_mcvs = true;
+		}
+
+		if (use_mcvs)
+			get_stats_slot_range(&sslot, opfuncoid, &opproc,
+								 collation, typLen, typByVal,
+								 &tmin, &tmax, &have_data);
 		free_attstatsslot(&sslot);
 	}