You are correct. Some PSU manufacturers put ridiculous amounts of power capacity on the 3.3 and 5Vdc lines but rob the 12Vdc rails in the process just so they can call it a 400W (or whatever) supply. You will need to upgrade to a "decent" (by decent, I mean certified 80% efficiency) PSU made by the likes of Seasonic or Antec.
I'm not very good with PSU's, but I have a PNY GTX 550Ti, and it works very well with my 450W PSU. If you aren't certain of how it will work and you know your specs, you can use this website, which is very helpful.