Modding Sprites: Getting the background to disappear

[EternalSpearman]

In Adobe Photoshop Elements, how do I get the background around the sprite to disappear? For instance, I cut and paste an image from the game into Photoshop, and modify it. However, a backgrond is still left over around the sprite, which makes the sprite look strange in battle, recruitment, etc screens. How do I get background to disappear? I've tried making the surroundings of the sprite transparent, but targa format doesn't support transparency.