Total newbie here. How can I get the MAX of the AVG?

Here's how I can get the mean...

SELECT AVG(x),par1,par2 FROM results GROUP BY par1,par2,par3;

Then I want the MAX of that across par3. The following does not compute, but could perhaps help to explain what I want...

SELECT MAX(AVG(x)),par1,par2 FROM ?the-query-above? GROUP BY par1,par2;

? but how? I have tried to look into subqueries... I just have problems moving from sequential programming... heeeeelp!