When edges line up Boolean weirdness ensues!

I was having a hard time getting the boolean modifier to work properly. My first problem was I didn’t realise the notch cutter object remained after the operation; I had to watch the video a couple times and play around with the visibility of the mesh objects before I saw what was going on, but I get it now!

When it came time to make the notch I dropped a rectangle in and voila! It worked! But… look at all those extra faces… If I lined up the bottom of the notch with the edges in the top of the bishop I’d have fewer polygons… When I did that I ended up with extra edges on the surface of the bishop that formed the outline of the notch, along with the floor of the notch inside. That was not at all what I was expecting.

Any pearls of wisdom about that?

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