Here's a tip for later in the game, but it's basically a spoiler because it makes a really hard part of the game so much easier.
When you are doing a base assault:
Just keep all your guys stationed in the upper area of the elevator shaft, stationed in strategic positions. Every turn, send a hovertank down the shaft to check all directions and then send it back up and out of the way. If it saw any aliens, use a mind probe on them to see their importance. You want to stun and capture the alien base commander so when you finally see him your guys with stun launchers are ready to take him out. The other guys just waiting their should easily be able to pick off any aliens you see with few if any casualties.