Flattening parts with glass-backed sandpaper (what to avoid)

In the past, I've used sandpaper that has been glued or double-stick taped to a large piece of glass to flatten small parts. Apparently, this only works well when the sandpaper is stationary and the part is moved. The part will naturally be flattened by the random passes on the sandpaper.
I tried to adapt this technique where the glass was moved and the part was stationary. It didn't work. The part ended up very smooth, but not flat. It's too difficult (apparently) to hold the glass at the same exact orientation for every stroke. I ended up mounting the part back in the mill and using a wide diameter end mill to flatten and smooth the surface in one pass.