How to fix new chain that switches gears when pedaling backwards I just recently replaced a chain that got incredibly beat up in the winter (it was rusted, and practically stiff when I removed it.)

I removed links from the new chain to match the length of the previous chain. The previous chain was the manufacturer installed stock chain.

It is a 3*8 - 24 speed configuration. I usually leave the front derailleur on 3, and make all adjustments on the rear.

If my bike is on the 4th cog or larger (so 4,3,2,1), the chain will "slip down" to the smaller cog if I pedal backwards.

So for example, if I am in 3x4, and I pedal backwards, the chain slips to 3x5. It corrects itself as soon as I start pedaling forward. If I try to pedal backwards any farther though, the chain just wraps around on itself and falls off.

The bigger the rear cog (for instance 3x1 or 3x2) - the slower I need to pedal for it to slip.

All comments &amp; answers are much appreciated :)
I consider it standard practice to replace the rear cogs at the same time as buying a new chain. If you don't the rear cog's teeth start to look like shark fins after a while and your chain will "climb". Esp. when pedaling backwards. 

Edit: worn cogs, even if they don't cause immediate problems, will stretch your chain causing it to wear out quickly.