Bulldogs World

We recently adopted a 4 year old rescue.  He was an outside dog prior to us having him.  He is doing wonderfully with his training, except at night.  He is crated at night (which he seems to love) b/c he goes in there to nap during the day and willing goes in to sleep at night, however, every morning when I get up to let him out, he has peed in his crate, on his bedding.  I have tried a smaller crate and it did not make a difference.  I let him out as late as 1 a.m. then out again at 6 when we wake up and still he has peed.  He goes longer during the day w/out peeing so I don't think it's bladder control.  Any suggestions?  Thanks!