How do I efficiently kill Handymen?

On my normal difficulty playthrough, the only thing that really gave me trouble was the Handymen. They seem to have a counter-attack for every strategy, and it takes a lot of firepower to bring them down, regardless of your weapons.

Now that I'm on 1999 mode, I know that these guys are going to be more or less impossible unless my aim is true and my strategy flawless. What strategies can I employ to take down Handymen more easily?