Magento resize() image quality: dirty white background

Question

I have a client who is seriously unhappy with the way their product thumbnails are rendering on Magento.

The dodgy appearance is noticeable on two accounts:

Answer 1

I had problems with images quality on one of projects. But the problem was not on back-end, but on the front-end. Images had bad quality because images width and height given in the CSS was not the same as the image file had.