diff --git a/src/backend/access/heap/vacuumlazy.c b/src/backend/access/heap/vacuumlazy.c
index 1bbc4598f7..243cdaa409 100644
--- a/src/backend/access/heap/vacuumlazy.c
+++ b/src/backend/access/heap/vacuumlazy.c
@@ -594,6 +594,19 @@ heap_vacuum_rel(Relation onerel, VacuumParams *params,
 	new_frozen_xid = scanned_all_unfrozen ? FreezeLimit : InvalidTransactionId;
 	new_min_multi = scanned_all_unfrozen ? MultiXactCutoff : InvalidMultiXactId;
 
+	/*
+	 * Another corner case is that if the relation is physically zero-length,
+	 * we don't want to record relpages=reltuples=0 in pg_class; what we want
+	 * to record is relpages=1, reltuples=0.  This tells the planner that the
+	 * relation has been seen to be empty by VACUUM or ANALYZE, so it should
+	 * not override a small measured table size.
+	 */
+	if (new_rel_pages == 0)
+	{
+		Assert(new_live_tuples == 0);
+		new_rel_pages = 1;
+	}
+
 	vac_update_relstats(onerel,
 						new_rel_pages,
 						new_live_tuples,
diff --git a/src/backend/access/table/tableam.c b/src/backend/access/table/tableam.c
index 4b2bb29559..0a92450e8a 100644
--- a/src/backend/access/table/tableam.c
+++ b/src/backend/access/table/tableam.c
@@ -585,11 +585,9 @@ table_block_relation_estimate_size(Relation rel, int32 *attr_widths,
 	 * doesn't happen instantaneously, and it won't happen at all for cases
 	 * such as temporary tables.)
 	 *
-	 * We approximate "never vacuumed" by "has relpages = 0", which means this
-	 * will also fire on genuinely empty relations.  Not great, but
-	 * fortunately that's a seldom-seen case in the real world, and it
-	 * shouldn't degrade the quality of the plan too much anyway to err in
-	 * this direction.
+	 * We test "never vacuumed" by seeing whether relpages = 0.  VACUUM and
+	 * ANALYZE will never set relpages to less than 1, even if the relation is
+	 * in fact zero length.
 	 *
 	 * If the table has inheritance children, we don't apply this heuristic.
 	 * Totally empty parent tables are quite common, so we should be willing
diff --git a/src/backend/commands/analyze.c b/src/backend/commands/analyze.c
index 924ef37c81..f0247e350f 100644
--- a/src/backend/commands/analyze.c
+++ b/src/backend/commands/analyze.c
@@ -620,6 +620,16 @@ do_analyze_rel(Relation onerel, VacuumParams *params,
 
 		visibilitymap_count(onerel, &relallvisible, NULL);
 
+		/*
+		 * As in VACUUM, replace relpages=reltuples=0 with relpages=1,
+		 * reltuples=0.
+		 */
+		if (relpages == 0)
+		{
+			Assert(totalrows == 0);
+			relpages = 1;
+		}
+
 		vac_update_relstats(onerel,
 							relpages,
 							totalrows,