From everything I have read this is what Ive gathered. (although this is for Oregon)
Check your court papers, see if in them anywhere it mentions removing the debt from report or anything to that effect. (some do say they are to be removed once paid)
If it was a valid judgement and you paid it all you can do is wait for it to fall off your report if it does not say to remove after pay in full in your papers.
Pretty much same boat I am in, I have read up on everything for months and it seems once you pay a judgement if your court papers dont have in there to remove it once paid its staying on your report until the statue of limitations runs out =/ Maybe someone from Louisiana will chime in with some more detailed info.
