Credit card company will not take the late payment marks off my report.

Hello,
My name is "Fix My Credit Report" and I came across your web site which by the way I think has an amazing amount of information that I have found to be very use full. I did however have a few questions for you. I went from having perfect credit to not so perfect credit when I got unengaged. Right now all my credit card bills are payed off but when I called my credit card company's to see if they would take these things off my report they said no. I am also having trouble establishing new credit. I have 1 credit card now that I pay on time, my car loans etc are all payed on time, but I need to know how to up my credit rating at a pretty fast rate. Any advice?
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Bo Majors / to Need better credit / show details / May 10
We must have 1 year of open and good credit. Better to have 2 years from today back.
Must haves'
Everything thing else seems ok
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Fix My Credit Report please / to me / show details / May 10
Thanks so much for getting back to me so soon. So even if just 1 credit card it will be ok. Does it look bad to have those accounts that were payed in full but closed? And is there anything else I Can do to build more credit faster?
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Bo Majors / to Fix my credit report / show details / May 10
We all need 3 good open lines of credit to keep good scores.
The paid off accounts dont hurt but don't help either.