Gotta say I really don't like all these sites that re-encode images (even more so with videos) and claim that "we can reduce filesize with, like, no quality loss using our Super Duper Compression Magic!" Because no, it's not magic, you're just re-encoding images, and possibly doing lossless optimizations on top of that (though who knows, they might even think the re-encoding is all the "optimization" an image might need already). Just look at this quick comparison I made, you can clearly see the JPG compression artifacts in the TinyJPG "optimized" version (which turned my optimized 1.27MB original JPG into a crummy-looking 431KB JPG): http://screenshotcomparison.com/comparison/101286 (this is a crop from the original image).

Rather than letting a service re-encode your images, you should rather use something that just optimizes them in an actual lossless fashion (optipng, mozjpegtran, or any service that makes use of these), and if you want to squeeze them to an even smaller size in a lossy fashion, then just save your JPGs at lower quality yourself or quantize your PNGs in a controlled fashion (pngquant does a pretty great job with that) - this is especially true with the latter, because haphazard color reduction with PNGs can lead to completely awful-looking results with higher-res images with lots of colors. Here's a comparison for that too: http://screenshotcomparison.com/comparison/101289

Bottom line: Feel free to apply lossless optimizations to your heart's content, but anything more than that you're better off just saving to lower JPG quality yourself to begin with (you'll get better results this way too since you're doing just a single lossy encode instead of two) or quantizing your PNGs yourself, provided you actually care about the quality of your images.

EDIT: Figured I could post some more images.

1. Original source image: http://blisswater.info/images/tiny/original.png (4987 KB) 2. JPG quality 90 encode: http://blisswater.info/images/tiny/encoded-q90.jpg (1033 KB) (encoded with ImageMagick using convert original.png -quality 90 encoded-q90.jpg) 2. Optimized JPG Q90: http://blisswater.info/images/tiny/encoded-q90-optimized.jpg (978 KB) (lossless optimization with mozjpegtran -copy none -outfile encoded-q90-optimized.jpg encoded-q90.jpg) 4. TinyJPG result with original.png as source: http://blisswater.info/images/tiny/encoded-tinyjpg.jpg (1581 KB) 5. TinyJPG result with encoded-q90.jpg as source: http://blisswater.info/images/tiny/encoded-q90-tinyjpg.jpg (485 KB)

As you can see by comparing 2 and 5, there is a very notable quality loss as a result of the TinyJPG re-encode. What's even more interesting is that if you want to avoid double conversion by uploading JPGs, TinyJPG will actually quantize your PNGs first (like their TinyPNG service does), as can be seen in 4 - this is something I was not expecting and find rather baffling as it quite notably alters the source image on its own even before the JPG compression.