Quote like you mean it

Changing the background/color/font of the quoted text. I know there's a CSS entry for that and I'm gonna find it, perhaps. While we are on the subject, can something be done about the overly prominent h1 or even h2 headers that appear in some quotes? Sure, I can demote them like a baby - just strip them of their html tags - but maybe there is a gentler CSS way to turn quoted headers less potent? It doesn't make a difference whether a header is quoted or not, right?