Cropping Custom Header Images

I uploaded an image that was sized to be as small or smaller than the default header image. However, the crop and publish function still required me to crop the image no matter how small (in pixels) I made it. Furthermore, if I did try to crop and publish, the option limited me to just moving the proposed “crop” over the image instead of a true crop function. I am sure there must be a work around, but I don’t know what it is. Please advise.