diff --git a/contrib/amcheck/verify_nbtree.c b/contrib/amcheck/verify_nbtree.c
index 767d8e9e1e..afbcd8ce76 100644
--- a/contrib/amcheck/verify_nbtree.c
+++ b/contrib/amcheck/verify_nbtree.c
@@ -350,11 +350,20 @@ bt_check_every_level(Relation rel, Relation heaprel, bool readonly,
 
 	if (state->heapallindexed)
 	{
+		int64		total_pages;
 		int64		total_elems;
 		uint64		seed;
 
-		/* Size Bloom filter based on estimated number of tuples in index */
-		total_elems = (int64) state->rel->rd_rel->reltuples;
+		/*
+		 * Size Bloom filter based on estimated number of tuples in index,
+		 * while conservatively assuming that each block must contain at least
+		 * MaxIndexTuplesPerPage / 5 non-pivot tuples.  (Non-leaf pages cannot
+		 * contain non-pivot tuples.  That's okay because they generally make
+		 * up no more than about 1% of all pages in the index.)
+		 */
+		total_pages = RelationGetNumberOfBlocks(rel);
+		total_elems = Max(total_pages * (MaxIndexTuplesPerPage / 5),
+						  (int64) state->rel->rd_rel->reltuples);
 		/* Random seed relies on backend srandom() call to avoid repetition */
 		seed = random();
 		/* Create Bloom filter to fingerprint index */
@@ -398,8 +407,6 @@ bt_check_every_level(Relation rel, Relation heaprel, bool readonly,
 		}
 		else
 		{
-			int64		total_pages;
-
 			/*
 			 * Extra readonly downlink check.
 			 *
@@ -410,7 +417,6 @@ bt_check_every_level(Relation rel, Relation heaprel, bool readonly,
 			 * splits and page deletions, though.  This is taken care of in
 			 * bt_downlink_missing_check().
 			 */
-			total_pages = (int64) state->rel->rd_rel->relpages;
 			state->downlinkfilter = bloom_create(total_pages, work_mem, seed);
 		}
 	}