I'm looking for a word or, more likely, a phrase--along the lines of "Hobson's choice," "busman's holiday," or "Pyrrhic victory"--to describe a problem that isn't really a problem. An example might be the "problem" of having too much evidence for something you are trying to prove.
"First-world problem" comes pretty close to what I'm looking for, but I'd appreciate a phrase that telegraphs a more focused irony and is perhaps a bit more sophisticated.