Actually, I read an interesting thing about no-kill shelters somewhere saying that some of them will take their animals to the "other" shelters...so they don't kill them, but the other shelter ends up doing so. I don't know how many or how common this is, I just found it interesting and unsurprising.

I personally would choose to go to a shelter that does euthanise when they reach capacity. I mean, you're not really saving a life if the animal is allowed to be in the no-kill forever.

Edit: Let's call them "Picky shelters", because they can pick and choose the animals they take in so they don't have to euthanise them.