Well, I had to solve it myself after all (and to be honest, VMware with Windows NT is a way to run IE 6 under Linux, but it really hurts - and it's incredibly slow).

What was it? Well, IE 6 doesn't support child selectors. That was it. I replaced the child selectors with descendant selectors, and it works. Child selectors express an exact and direct dependency: an A tag that sits directly inside an H2 tag is selected by the selector H2>A. Descendant selectors express a relative dependency: an A tag that sits somewhere inside an H2 tag is selected by H2 A. But there can certainly be more between H2 and A in the HTML code. A code like

Title

would not select the links with child selectors, but it would with descendant selectors.

In this case I could easily change it, since I generally want all links within the headings in white anyway, not just the direct links - so to speak my stylesheet wasn't correct, because if I had ever introduced a span or something, it would have broken.

Still, it's annoying when a browser simply doesn't implement a feature ... All defined selector forms are documented at the W3C. Bugs with IE regarding selectors can be found for example in this bug list.