Changing source of Excerpt text

Hi! On my home page, I like that Excerpt text is shown for my posts, for instance in the Feature Slider. I know how to change the number of words shown, or to turn it off completely. Can I change what words are shown in the Excerpt? It seems that by default it takes the first x number of words from the beginning of the article. But I find that this isn't necessarily appropriate for an Excerpt. For example, if the start of the article contains headings, or a table of contents. Thanks.