diff --git a/src/backend/access/nbtree/nbtutils.c b/src/backend/access/nbtree/nbtutils.c
index 2e896a258f..f87eadcdec 100644
--- a/src/backend/access/nbtree/nbtutils.c
+++ b/src/backend/access/nbtree/nbtutils.c
@@ -325,8 +325,14 @@ _bt_preprocess_keys(IndexScanDesc scan)
 
 			/*
 			 * If = has been specified, all other keys can be eliminated as
-			 * redundant.  In case of key > 2 && key == 1 we can set qual_ok
-			 * to false and abandon further processing.
+			 * redundant.  If we have a case like key = 1 AND key > 2, we can
+			 * set qual_ok to false and abandon further processing.
+			 *
+			 * We also have to deal with the case of "key IS NULL", which is
+			 * unsatisfiable in combination with any other index condition.
+			 * By the time we get here, that's been classified as an equality
+			 * check, and we've rejected any combination of it with a regular
+			 * equality condition; but not with other types of conditions.
 			 */
 			if (xform[BTEqualStrategyNumber - 1])
 			{
@@ -339,6 +345,13 @@ _bt_preprocess_keys(IndexScanDesc scan)
 					if (!chk || j == (BTEqualStrategyNumber - 1))
 						continue;
 
+					if (eq->sk_flags & SK_SEARCHNULL)
+					{
+						/* IS NULL is contradictory to anything else */
+						so->qual_ok = false;
+						return;
+					}
+
 					if (_bt_compare_scankey_args(scan, chk, eq, chk,
 												 &test_result))
 					{
diff --git a/src/test/regress/expected/create_index.out b/src/test/regress/expected/create_index.out
index c78d9ee1e8..b23c712204 100644
--- a/src/test/regress/expected/create_index.out
+++ b/src/test/regress/expected/create_index.out
@@ -1279,6 +1279,18 @@ SELECT count(*) FROM onek_with_null WHERE unique1 IS NULL AND unique2 IS NOT NUL
      1
 (1 row)
 
+SELECT count(*) FROM onek_with_null WHERE unique1 IS NOT NULL AND unique1 > 500;
+ count 
+-------
+   499
+(1 row)
+
+SELECT count(*) FROM onek_with_null WHERE unique1 IS NULL AND unique1 > 500;
+ count 
+-------
+     0
+(1 row)
+
 DROP INDEX onek_nulltest;
 CREATE UNIQUE INDEX onek_nulltest ON onek_with_null (unique2 desc,unique1);
 SELECT count(*) FROM onek_with_null WHERE unique1 IS NULL;
@@ -1305,6 +1317,18 @@ SELECT count(*) FROM onek_with_null WHERE unique1 IS NULL AND unique2 IS NOT NUL
      1
 (1 row)
 
+SELECT count(*) FROM onek_with_null WHERE unique1 IS NOT NULL AND unique1 > 500;
+ count 
+-------
+   499
+(1 row)
+
+SELECT count(*) FROM onek_with_null WHERE unique1 IS NULL AND unique1 > 500;
+ count 
+-------
+     0
+(1 row)
+
 DROP INDEX onek_nulltest;
 CREATE UNIQUE INDEX onek_nulltest ON onek_with_null (unique2 desc nulls last,unique1);
 SELECT count(*) FROM onek_with_null WHERE unique1 IS NULL;
@@ -1331,6 +1355,18 @@ SELECT count(*) FROM onek_with_null WHERE unique1 IS NULL AND unique2 IS NOT NUL
      1
 (1 row)
 
+SELECT count(*) FROM onek_with_null WHERE unique1 IS NOT NULL AND unique1 > 500;
+ count 
+-------
+   499
+(1 row)
+
+SELECT count(*) FROM onek_with_null WHERE unique1 IS NULL AND unique1 > 500;
+ count 
+-------
+     0
+(1 row)
+
 DROP INDEX onek_nulltest;
 CREATE UNIQUE INDEX onek_nulltest ON onek_with_null (unique2  nulls first,unique1);
 SELECT count(*) FROM onek_with_null WHERE unique1 IS NULL;
@@ -1357,6 +1393,18 @@ SELECT count(*) FROM onek_with_null WHERE unique1 IS NULL AND unique2 IS NOT NUL
      1
 (1 row)
 
+SELECT count(*) FROM onek_with_null WHERE unique1 IS NOT NULL AND unique1 > 500;
+ count 
+-------
+   499
+(1 row)
+
+SELECT count(*) FROM onek_with_null WHERE unique1 IS NULL AND unique1 > 500;
+ count 
+-------
+     0
+(1 row)
+
 RESET enable_seqscan;
 RESET enable_indexscan;
 RESET enable_bitmapscan;
diff --git a/src/test/regress/sql/create_index.sql b/src/test/regress/sql/create_index.sql
index 31b49ca227..bf27379f59 100644
--- a/src/test/regress/sql/create_index.sql
+++ b/src/test/regress/sql/create_index.sql
@@ -451,6 +451,8 @@ SELECT count(*) FROM onek_with_null WHERE unique1 IS NULL;
 SELECT count(*) FROM onek_with_null WHERE unique1 IS NULL AND unique2 IS NULL;
 SELECT count(*) FROM onek_with_null WHERE unique1 IS NOT NULL;
 SELECT count(*) FROM onek_with_null WHERE unique1 IS NULL AND unique2 IS NOT NULL;
+SELECT count(*) FROM onek_with_null WHERE unique1 IS NOT NULL AND unique1 > 500;
+SELECT count(*) FROM onek_with_null WHERE unique1 IS NULL AND unique1 > 500;
 
 DROP INDEX onek_nulltest;
 
@@ -460,6 +462,8 @@ SELECT count(*) FROM onek_with_null WHERE unique1 IS NULL;
 SELECT count(*) FROM onek_with_null WHERE unique1 IS NULL AND unique2 IS NULL;
 SELECT count(*) FROM onek_with_null WHERE unique1 IS NOT NULL;
 SELECT count(*) FROM onek_with_null WHERE unique1 IS NULL AND unique2 IS NOT NULL;
+SELECT count(*) FROM onek_with_null WHERE unique1 IS NOT NULL AND unique1 > 500;
+SELECT count(*) FROM onek_with_null WHERE unique1 IS NULL AND unique1 > 500;
 
 DROP INDEX onek_nulltest;
 
@@ -469,6 +473,8 @@ SELECT count(*) FROM onek_with_null WHERE unique1 IS NULL;
 SELECT count(*) FROM onek_with_null WHERE unique1 IS NULL AND unique2 IS NULL;
 SELECT count(*) FROM onek_with_null WHERE unique1 IS NOT NULL;
 SELECT count(*) FROM onek_with_null WHERE unique1 IS NULL AND unique2 IS NOT NULL;
+SELECT count(*) FROM onek_with_null WHERE unique1 IS NOT NULL AND unique1 > 500;
+SELECT count(*) FROM onek_with_null WHERE unique1 IS NULL AND unique1 > 500;
 
 DROP INDEX onek_nulltest;
 
@@ -478,6 +484,8 @@ SELECT count(*) FROM onek_with_null WHERE unique1 IS NULL;
 SELECT count(*) FROM onek_with_null WHERE unique1 IS NULL AND unique2 IS NULL;
 SELECT count(*) FROM onek_with_null WHERE unique1 IS NOT NULL;
 SELECT count(*) FROM onek_with_null WHERE unique1 IS NULL AND unique2 IS NOT NULL;
+SELECT count(*) FROM onek_with_null WHERE unique1 IS NOT NULL AND unique1 > 500;
+SELECT count(*) FROM onek_with_null WHERE unique1 IS NULL AND unique1 > 500;
 
 RESET enable_seqscan;
 RESET enable_indexscan;