Unique index or not

Dear all, Suppose I have a table with three columns: col1, col2, col3. For data integraty constraint, there is a unique index created for col1. For query performance, I need to add an composite index on col1, and col2, Which type of index you would suggest to add: unique or duplicate? I think the uniqe type is unnecessary and has a bigger impact on insert. But I'm not sure whether it has advantage over the duplicate type on select. Any comments? Cheers.