What is the quickest Mac OS X app to use to remove the background of an image to make it transparent? I followed the instructions in How to use Preview for Basic Image Editing: Remove Backgrounds and Extract Shapes to use the Preview app to remove backgrounds with an image. The problem is that the "Instant Alpha" tool sometimes does not capture all the pixels and can't figure out how to use the rectangle tool to remove those remaining pixels. I tried highlighting the pixels and then pressing delete but it doesn't work. Can someone explain how to do it or recommend another free, lightweight Mac OS X tool to remove background to make it transparent? I do not want to use Photoshop or anything else expensive.
Just selecting an area and hitting delete just as you do with the Alpha tool should do it fine.  I tend to get a good outline with the alpha tool, then zoom in and use the lasso selection tool to draw around any stray pixels - remember to complete the lasso yourself, or it may complete it for you and if the end is not near the start, it will just draw a big line between the 2 across whatever is in its way.

You don't say what OS you are using, but I've done it this way in every OS since Tiger...