How to keep XSLT from introducing whitespaces in HTML output

I am generating HTML from XML sources using XSLT. The HTML shows a lot of whitespace that was not in the original XML files. Normally this is not a problem as the browser will ignore the extra whitespace characters. But I am developing an application that relies on correct positioning of the text cursor inside the HTML page. The added whitespaces do mess up the offsets, making it impossible to reliably position the cursor inside an element.