You'll want to visit the rebuilding forum and do some reading there about the removal of negative items. Basically you are going to be asking for goodwill adjustments to those accounts, something that can be done with letters, phone calls, emails, etc. Many times you'll get a ton of "no" responses saying that they won't/can't do what you're asking, but over time with enough persistence most people to find success.
Keep working with BBS. He knows all about derogs (and lots of other stuff).
Just to keep you moving along, and as I am sure BBS will confirm, the Goodwill Letter strategy is not in any way like a dispute. The dispute process is for when there is something on your report that you are certain is false. In your case, you are certain it is true -- it's just that you'd really love it if the original creditor would have a soft heart toward you and reach into the bureau's database and delete that bad mark. Creditors can do that but they have no legal obligation to do so, which is why the Goodwill Letter strategy can take many months (years?) to work.
CGID is exactly right above. A dispute is very different than a GW adjustment request. Since you are sure that the late payments associated with your loan are in fact accurate, you do not want to dispute them. If your lenders see that you're disputing accurately reported information, they may put a notation on your account(s) regarding that, which could in turn make your future GW requests more difficult. Disputes if they aren't legitimate only waste the time of the lender and can thus be a cause of irritation; that's not what you want when you're going to be asking them for a favor (GW adjustment).
Here's a thread I suggest you check out once you write your first GW letter. There are lots of threads in the rebuilding section that discuss how to write a GW letter and the thread below sort of picks up after that point on how to get it out there to as many people as possible.