this probably sounds like a lengthy explanation but it is very simple o do and is very effective.
Effective, but it's not really a compression method. I find that, on 1152x864 desktop resolution, with 17" monitor, anything below 800x600 pixels just looks too small on the screen. I know for a fact that there will be a good deal of people with higher resolutions/smaller monitors than me, and so the size of the picture will be reduced ever more.
Whatever it may be, screenshots or photos, if I'm posting them online, I'll stick them at 800x600.
Back to the original question...
You may find that when shrinking an image in Irfanview, it tends to make the picture much softer than before. This can also give the impression of heavy compression (no rhyme intended!), what with the edges in the picture being less defined. The best thing to do, is to find a program that doesn't soften the images (i.e. Photoshop, or any freeware alternative), resize the image, then open it up in Irfanview and compress.