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Can't you just hit the little multi-box icon on the bottom right always (to the right of the home icon)? Then swipe an app away to kill it.

Not available on some earlier Android versions — but a nice way to handle it.

My understanding is that this does not kill the app, merely removes it from the list.

It kills the app on my phone (Nexus 4 Cyanogenmod). If I ever get a slowdown I open up the switcher and swipe away all my recent apps to close them.