If you need no credit limit at all, just SM them to reduce the credit limit to the lowest it can be, then you'll find out.

I've heard (and experienced) that it can be (temporarily) detrimental to your credit score to have more than 30% of the your credit limit used on any particular card in any particular month. So I generally don't lower to less than $3k if I've got close to $1k in charges that are not paid off yet.

Keep in mind that if the card started out with, say, for example, $11k of CL, and you lower it to $3k vs lowering it to $2k, there's not much difference between those. What's signficant is that you lower it by many thousands.

Also, keep in mind that it can take (many?) weeks before the CL you lowered becomes available for a new card. So it may be better to lower to a less drastic degree sooner (while you're still doing the minimum spend) rather than wait until the last minute to lower it the most possible (in one step). To that end, I lowered by last WE to $6k first, and then when I had less than $1k of charges left, I lowered it again to $3k. If the lowering to $3k was "too soon" before my next W app, at least the lowering to $6k made a couple months earlier should help.