As a side note, don't make the mistake of assuming that you have to choose between being really good at one thing or being acceptable at many things. It's possible to be really good at many things.
I run into this problem all the time with recruiters, especially non-technical recruiters, who are the kind of people who just want to match up YEARS_EXPERIENCE_NEEDED with ${ACRONYM} down a list, and if you don't match up, you're filtered out. It's very frustrating because it's hard to get interviews, which is where I have a chance to shine, and show that client why taking on someone with a broad skillset -- especially one who understands business issues -- is better than hiring a hyper-specialized candidate.