Complicated GROUP BY

Dear All,

I have the following problem with grouping: I want to know the maximum
in a group as well as the maximal element. Example:

I have a table products_providers:
product | provider | criteria_1 | criteria_2

I have a number of products, each of them from a several providers.
Each product is described by two numeric values. I can easily select
the best value for each product by a given criteria, like:

select product, max(criteria_1) from products_providers group by
product;

but I need to know the best-scoring provider as well.

Result I need should look like:
product | best_provider_1 | best_criteria_1 | best_provider_2 |
best_criteria_2

If it counts results may be split into two tables: one for the first
and the other for the second criteria

Can you help me with a painless solution?
Dominik