Well, I've learned one thing. Maybe I should have known. Only Lights 1 and 2 cast a shadow, and when I had only one light it was a number 3, the others having been deleted. That explains the no-shadow mystery. I've noticed a light flipping again while rendering and can easily duplicate it, but it seems to be some other light than a Number 1 or 2, in which case the shadow is unaffected. I hope you followed all this. Thanks for the help. Poser lights are temperamental to say the least.