This jester weighed in at the starting line as a 65.7k JPEG file.
Photoshop Save for Web reduced my JPEG jester to 16k so I could show him here without too much strain on your bandwidth.
There are times when you need an even smaller picture. I Saved it for Web in Photoshop as a GIF at 5.7k by throwing out all but 15 colours.
As you see, I didn't lose too much quality - and I had reduced the file size by 60 kilobytes.
Try this with a photo and you'll find it curdles the colours, giving it a rather crude, posterized look. JPEGs preserve the subtleties of shading. GIFs work best for drawings with areas of flat colour.
You can cut the number of colours in GIF computer images - often quite drastically - and with them file size. Your computer image still looks good, and avoids that machine-turned look you get with a vector image.
A really good tool for reducing image size is Photoshop (or Photoshop Elements, miles cheaper and surprisingly powerful). If you have Photoshop, you simply choose to save your image with Save for Web.
Can you crop your picture? Have a go with the crop tool. Make sure the proportions are about the same as your chosen format.
Removing the background from a portrait can save file space as well as highlighting your subject.
If you want the background to be transparent, fill it now with a colour that doesn't appear anywhere else in your picture. When you save for the web as a .gif, you'll be able to replace that colour with see-through pixels.
Next, go to your Image drop down menu - Image Size. (There is a pixel size reducer in the Save for Web screen, but you have more control if you reduce it here.) Choose your pixel dimensions.
Make sure you have 'Constrain proportions' selected if it's a portrait, or your subject may look like a reflection in a fairground mirror! If one side is still too short, go to Canvas Size and add a bit on, rather than distorting your favourite face. You can always fill in the added strip with the Clone Stamp.
Be sure to keep your original graphic and save the edited version via Save for Web with a new name. Then you willl always be able to revert if you decide your downsize was a bit over-enthusiastic.