I avoid using JPEGs whenever I can. I know there are pros and cons for doing so, and JPEG has its merits, so please don't argue that here.

Anywho, a lot of applications will accept several different file formats, but then convert them all to JPEG. This gives my Avatars lots of nasty artifacts.

Is there a certain trick to reducing these artifacts?

jpg is mostly blur, so "preblurring" the images might help having faithful copies in jpg later. Also, even if the application is making a jpg, you should be able to choose the compression, and at no compression, jpg is, for all purposes, a bitmap, so there should be no problem with artefacts.
I propose you make the jpg youself, out of a bmp, by using IrfanView or similar programs, that allow you to specify the number of pixels and amount of compression. then you can import it into the appklications that misbehave, and it might be better.

If you like, you could post some file, and specify the way it should come out (a x b pixels) and we here on the forum could try some ourselves, and give you some feedback and suggestions

SureWhyNot wrote:Anywho, a lot of applications will accept several different file formats, but then convert them all to JPEG. This gives my Avatars lots of nasty artifacts.

Is there a certain trick to reducing these artifacts?

I don't think there's any rules of thumb when designing an image to reduce artifacts when you can't control the compression. Although I'm sure some effects can make artifacts more obvious, such as putting blocks of red beside block of blue. Compression artifacts are less obvious in real photos then on clipart-type images, which is why you should use GIF for images with few colours--so knowing that, you could suggest using photos for your avatar

Having said that, whilst most applications will convert a non-JPG into a JPG, if you provide a JPG in the first place then some applications will not re-convert it (but I know some will). My recommendation is to convert your picture to a JPG yourself then try submitting it.