> SELECT * FROM huge_table h, tiny_table t WHERE UPPER( h.id ) =
> UPPER( t.id )

What about :

SELECT * FROM huge_table h WHERE UPPER(id) IN (SELECT upper(id) FROM
tiny_table t)

Or, try opening a cursor on your original query and using FETCH. It might
result in a different plan.
Or lower random_page_cost.

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TIP 5: don't forget to increase your free space map settings