JPEG is very good indeed, but it can't compete when transparency is needed.

I've chosen Lenna as an example image because it's a classic, rather than as an example where lossy PNG can't be beaten.

But take any transparent image from Apple.com, and you can halve its size: http://imgur.com/a/VLlqG

(and images from pngquant2 are even smaller, but there are few that become too lossy).