Displaying custom header image despite featured content slider

I currently use the featured content slider instead of a header, but I want certain pages to display one static image (or, if it’s any easier, a featured content slider with only one featured post). Is it possible to have the slider on certain pages and a static header on others?

I tried various ‘custom header’ plugins, but they did not work because the featured content slider always overrides the header image, whether or not it is a custom one.