Photoshop Transparent Background in CS5

I was trying to remove background from a couple of icons. Internet is full of articles that tell you to use the  Magic Wand then press Delete. I did it but instead of deleting the background it would show me the following dialog:



and whatever I did - changed Contents or Blending, changed Opacity - nothing helped. I simply cannot delete the background!

After an hour of agony I decided to try another tool - Background Eraser Tool and when I was opening it I accidentally noticed another tool - Magic Eraser Tool. Select it and click on your background - it's going to work.