The Bad Guys Need Attention Too

During my latest novel revision, I'm working on bringing out some of the secondary characters in my novel, including a villian.

It's so easy to rely on stereotypical villain traits and behaviours. Sneers. Evil stares. Rudeness. Threats, poisoning, locking the good guy away. I'm working on coming up with some truly unique ways to show his evil nature.

At the same time, I need to balance how much of his scheming to reveal. Since he's not the point of view character, I can't show his thoughts. His schemes are only obvious through his actions and the thoughts and reactions of the other characters. Neither one of these necessarily show the reasons for why he's behaving the way he does, even though the reader will eventually want to know.

Do you have any tips on creating a good villain?