Is it better to pay off current non-delinquent debt or my spouse's past credit delinquency?

We are trying to clean up our credit scores and are about to come into some money. We know we need to pay off some debt, but are unsure whether to pay off old delinquency's or if it is better to use that money to pay off my current credit cards. My credit score is fine, but I don't like having any debt. His credit score is not very good at all, but I'm not sure how much paying off the old delienquency will help.