I've just tried this in PostgreSQL for comparison on a table with 1000 rows and three columns (id, a TEXT, b TEXT) and indices on a and b.
```
wolfgang=> explain select * from t1 where (a = 'a500' or 'a500' is null);
QUERY PLAN
----------------------------------------------------------------
Index Scan using t1_a on t1 (cost=0.28..8.29 rows=1 width=12)
Index Cond: (a = 'a500'::text)
(2 Zeilen)
wolfgang=> explain select * from t1 where (a = 'a500' or 'a500' is null) and (b = null or null is null);
QUERY PLAN
----------------------------------------------------------------
Index Scan using t1_a on t1 (cost=0.28..8.29 rows=1 width=12)
Index Cond: (a = 'a500'::text)
(2 Zeilen)
wolfgang=> explain select * from t1 where (a = 'a500' or 'a500' is null) and (b = 'b500' or 'b500' is null);
QUERY PLAN
----------------------------------------------------------------
Index Scan using t1_b on t1 (cost=0.28..8.29 rows=1 width=12)
Index Cond: (b = 'b500'::text)
Filter: (a = 'a500'::text)
(3 Zeilen)
```
So here the behavior is as I expect, assuming that "Index Scan" means an index lookup - one index is used, and the other condition is either ignored (if the parameter is NULL) or applied as a filter. It seems to work exactly the same with parameters, like this:
```
PREPARE foo1 (text) AS SELECT * FROM t1 WHERE ($1 IS NULL OR a=$1);
EXPLAIN EXECUTE foo1('a500');
```