An understanding of graphics principles may help here ( as anywhere else).
WHY you want the size reduction is obvious, but why do you need lossless for the web? Are you posting files for the user to print and enlarge in hi-res ( this is generally a bad idea in EVERY SENSE). However you could solve this by using linked thumbnails, that is your page shows reduced, and compressed images, but the link is to the HR version.
Going back to JPEG format which is, by definition, LOSSY. It utilizes a grid system of 256 'patterns' ( these are the artifacts you start to notice when you over compress)
to which it tries to find a close match to the pixel arrangements in your image. Ironically, the larger the image the less noticeable these patterns are and the %wise compression you gain. Also because of this limited pattern method compression has what I call 'quantum quality nodes' depending on the dimension of your image and selected quality %)
This is what I mean:
An image that has dimensions that are multiples of 16px fares better quality wise that ones that do not, regardless of the compression level
You can observe this in PS's 'save for web' best, as it tells you what the final file size will be, but you only compress well w/o significant loss of quality at specific nodes ( I believe they are around 8/10% intervals.. but am not sure ). Example a 1MB uncompressed image, may reduce to 400bk at 95%(initial comp), 250kb at 85%, but 246KB at (78%) with significantly more quality loss than 85%, while 75% might give you a 200kb size with nearly the same quality as the 78% image. THESE #s are for the sake of explaining what i meant by QUANTUM QUALITY NODES only.
PNG-24is a lossless HQ format. I think of it as TIFFs for the web, :)) But just like tiffs file size is always much bigger. However, it was mentioned before that metadata, now often included in all image files , does tend to bloat file sizes. Which made think...
There are utilities out there (png as PNGcrush) which can remove not only the meta data from your PNG24 but the alpha channel ( which you probably don't need, if you were saving as jpg before) I will post again if any other such utilities come to mind.