"Throwing the baby out with the bathwater" means that something essential is lost in the process of getting rid of something unwanted (and relatively minor).
I'm looking for a phrase that means that one brings something greatly negative upon oneself in the process of obtaining something that is wanted (and relatively minor). Is there one?
EDIT: Slight elaboration: The phrase should mean that the process of obtaining A (the relatively minor positive thing) unavoidably brings with it B (the big negative thing). It is entirely possible that A might be obtained in another way, by the way.
As I write that, I think I know the phrase, but I'm not sure it exists in English (I'm Swedish). It is something to do with fixing minor problems with hand grenades, e.g. "Like fighting house rats with hand grenades". I don't know if there is an original, standard version however. Has anyone got an idea?