This article is an adaptation from my french seo blog on love-moi.fr
Google have announced his mobile first index, and the speed of a website will matter.
I was working on a demo Magento website with a lot of images but when I try to look at the pagespeed test on gtmetrix (because there's google pagespeed test and yslow test in the same panel), there was always a red flag on « image optimisation ».
The easy way if you're a sysadmin and have your own server, is to use mod_pagespeed. it works for apache and nginx. You just have to activate it, and let him do the job. You will have Grade A and nearly 100% on your pagespeed test.

If you are on a shared server, that's not the same, you can't install server scripts.
I was worry about pagespeed, it's like if he tell you : hey this is the optimize image I've done, you're a looser.
On my firebug developer tools, there's pagespeed and yslow, and for images, there was a link to smush-it, where you can download the optimized images.
That's what I've done : Download image, replace the old with the new ones, and it was ok, I've gt my 98% on pagespeed. But downloading files one by one, is not a good solution.

