Preview.app auto-descreening scanned imaged

Due to the way many colour printers work, when you scan a printed colour image you will often get a moire effect.

I find that when such scanned images are opened in Apple's Preview application it initially displays the image complete with moire patterns, and then a fraction of a second later redraws the image with much if not all of the moire patterns removed. This suggests it is automatically 'descreening' the image to improve the quality.

Note: This is a good thing.

However when Preview later is used to print the image, the moire pattern is returned. Is anyone aware of a way to get it to print better in this situation?

Note: I am aware that PhotoShop can cure all image ills, but not everyone can afford it.