[stan_rogers]

There's compressed and there's compressed. Two PNG-8 images may be perceptually identical (or at least close enough that youd need to overlay and switch between them to see the differences) but one has a 16-color palette and occupies less than 1K (and may be neatly tucked into a stylesheet as a data URI, saving a request) while the other is over 20K. Some JPEGs can barely take 4:1 compression, while others can stand 20:1 without artifacting. It depends on the amount of detail and local contrast. (Oh, and killing any extraneous EXIF data can save huge amounts of space without affecting compression.)

Is this really needed for mobile first design? I'd be inclined to say that it's more important for mobile-first since data transfer tends to be slower and more expensive. Remember data caps, whether hard or soft, and overage fees. Every byte you can save is worthwhile to a mobile user. Think of them as the modern equivalent to a dial-up user whose host connection is a long-distance number.