As mentioned in an earlier post by Rose, Murphy never pees or defecates in his inner "den": his large crate. But when he wakes up, he was immediately peeing outside the crate. So we've adopted Rose's strategy, effective as long as one can remain near to the area (easily enough done here as nearby we have two computers and a TV): when he's tired, we lock him in the cage. When he wakes up and whines, we take him right outside where he generally then pees and gets rewarded.