\part. I want it to look more or less like a section with a larger font. For this I use titlesec. It works fine, except that LaTeX will insert additional space if the part start at the top of a new page. Why is that and how can I avoid it?
Even though I use fancyhdr in my real document as well, it's actually not needed to reproduce the unwanted behavior. It's just convenient to have the header separator because it makes the enlarged space more easily visible.