Originally Posted by z415

Assuming you don't want to change parts, you can try to lose a link or two in the chain to increase tension or fine the screw in the backside of the RD that increases tension. I don't know the official name of the screw, but it is the one that you use when you want to bring your jockey wheels further from your cogs if they rub. If you remove a link, make sure you have enough links to cover the gear range you will use - some say enough to cover big cog/big ring, but I would think you wouldn't need that if you don't cross chain.

I had a similar problem when I went 1x9 on both my bikes, but after doing both those, I have no problems.