They chased each other for two hours.
No more mice problem.
I saw one mouse that was so big it was scary: Laurel could not kill it and it escaped.
This was two weeks ago. Have not seen the mice again.
Billy gets along marvelously well with the cats. He likes to sleep next to where they are sleeping. And he is learning to stay chill when they panic and run and play every which way up and down the stairs.