Useful indexes can use qualifiers

Matching index scans can use qualifiers that further restrict the result set. Remember that a WHERE clause that contains at least one optimizable predicate is optimizable. Nonoptimizable predicates can be useful in other ways.

Consider the following query:
WHERE orig_airport < 'BBB'
AND orig_airport <> 'AKL'
The second predicate is not optimizable, but the first predicate is. The second predicate becomes a qualification for which Derby evaluates the entries in the index as it traverses it.
Related concepts
What is an index?
What's optimizable?
Covering indexes
When a table scan Is better
Indexes have a cost for inserts, updates, and deletes