As a former Revenue Manager, I'll say that this is the biggest misconception about minimum stay controls. To know whether you're doing the hotel a favor by "giving back" a room to resell, you have to check the rate for the night you're not using. The vast majority of time, the night you don't want is going to be the "shoulder" night. That's a room that the hotel doesn't really need because they won't sell out anyway.

The easiest example is a weekend. If a hotel knows it can sell out both Friday and Saturday nights, they might place a minimum stay of 3 nights. If a guest decides they now don't need that Sunday, the hotel only makes money if they can resell that room for Sunday. But, for many hotels, Sundays are quietest night of the week. Since they never were turning away anyone needing Sunday, having that room back is a net loss in revenue.

So, instead of looking at the rates on the nights you'll use, check the rate for the night you don't need. If it's available for a 1-night stay at a lower rate, you're not helping out the hotel.

(I hope I explained that clearly.)