Remove uniqueness of index in PostgreSQL

You may be able to remove the unique CONSTRAINT, and not the INDEX itself.

Check your CONSTRAINTS via select * from information_schema.table_constraints;

Then if you find one, you should be able to drop it like:

ALTER TABLE <my_table> DROP CONSTRAINT <constraint_name>

Edit: a related issue is described in this question

I don't think it's possible... even in the pgAdmin III UI, if you try to edit a constraint created with your statement, the "Unique" box is greyed-out; you can't change it through the UI. Combined with your research on the ALTER INDEX docs, I'd say it can't be done.

Assume you have the following:

Indexes:
    "feature_pkey" PRIMARY KEY, btree (id, f_id)
    "feature_unique" UNIQUE, btree (feature, f_class)
    "feature_constraint" UNIQUE CONSTRAINT, btree (feature, f_class)

To drop the UNIQUE CONSTRAINT, you would use ALTER TABLE:

ALTER TABLE feature DROP CONSTRAINT feature_constraint;

To drop the PRIMARY KEY, you would also use ALTER TABLE:

ALTER TABLE feature DROP CONSTRAINT feature_pkey;

To drop the UNIQUE [index], you would use DROP INDEX:

DROP INDEX feature_unique;