FICO was able to shed some light on the question. The most important point made by spokesman Craig Watts is that it’s a myth that if you close a credit-card account, all trace of it disappears from your credit score. In fact, he says, the credit agencies from which FICO draws information used to calculate your score hold on to payment history for years — the positive stuff for about a decade and the negative stuff usually for seven years.

That information is used to calculate two parts of your credit score. One is payment history, which accounts for 35% of your score and which reflects, among other things, whether you made your payments on time and whether you welshed on any balance you may have owed when you chopped up your card. Another is length of credit history, accounting for 15% of your score, which reflects whether you’re a newcomer to paying people back or not.

All that stays, Watts says, if your card goes. You’ve read — perhaps from well-meaning people on FICO’s own message boards — that you should never close your oldest credit card because your length-of-credit-history measurement will immediately plummet? Again, that’s a myth, says Watts.

Where you may get into trouble right now is in the “amounts owed” area, which accounts for another 30% of your score. One important element of that is what’s called credit-card utilization — that is, the size of the balances you carry on your credit cards as a percentage of the amount you could theoretically borrow on all your cards. Imagine, for example, that you have two credit cards with $5,000 limits on each, with a $500 balance on one and a zero balance on the other. If you close the zero-balance account, you’ve gone from using 5% of your available credit (the $10,000 total on your cards) to 10% (of the $5,000 on the remaining card) — not a big deal in credit-card terms. In low-utilization situations such as that, closing an account should have virtually no effect on your credit score, says Watts. “No harm, no foul,” he says.

But let’s say instead that you have three $5,000-limit cards — one with a $3,000 balance and the others with none — and you drop your two zero-balance cards. In this case, your credit-card utilization rate will go from 20% to 60% — a noticeable amount that will certainly ding your credit score. How much? Can’t say, since we’re back to the black-box credit-scoring system.

In any case, Watts says that if you already have a score in the upper half of the 700s or above — that’s about 40% of the population — losing a few points shouldn’t hurt you at all, practically speaking.

So if you want to chop up your credit card, start chopping. The downside is probably a lot smaller than you think.