Can I add a UNIQUE constraint to a PostgreSQL table, after it's already created?

psql's inline help:

\h ALTER TABLE

Also documented in the postgres docs (an excellent resource, plus easy to read, too).

ALTER TABLE tablename ADD CONSTRAINT constraintname UNIQUE (columns);

Yes, you can. But if you have non-unique entries on your table, it will fail. Here is the how to add unique constraint on your table. If you're using PostgreSQL 9.x you can follow below instruction.

CREATE UNIQUE INDEX constraint_name ON table_name (columns);

If you had a table that already had a existing constraints based on lets say: name and lastname and you wanted to add one more unique constraint, you had to drop the entire constrain by:

ALTER TABLE your_table DROP CONSTRAINT constraint_name;

Make sure tha the new constraint you wanted to add is unique/ not null ( if its Microsoft Sql, it can contain only one null value) across all data on that table, and then you could re-create it.

ALTER TABLE table_name
ADD CONSTRAINT constraint_name UNIQUE (column1, column2, ... column_n);