Indexes on low cardinality columns

Folks,

We have just migrated from Oracle to PG.

We have a database that has approx 3 mil rows and one of the columns has a cardinality
of only 0.1% (3000 unique values).

We have to issue several queries that use this low cardinality column in a WHERE clause
as well as see this column participating in JOINS (ouch!).

A regular B-Tree index has been created on these columns.

In Oracle, we replaced the B-Tree Indexes with Bitmap indexes and saw performance go
through the roof. I know Postgres does not have Bitmap indexes,
but is there a reasonable alternative to boost performance in situations where low cardinality
columns are involved ?

I dont have the option of changing schemas - so please dont go there :)

TIA,
VK