I noticed on my last ride that when I shift the rear cogs from the larger cogs to the smaller cogs it's not a smooth shift. I took it home and shifted and watched what was happening, it seems when I shift there is a little bit of slack in the chain.

When I shift in the other direction is smooth as always, just when I'm putting the bike into a harder gear I'm having this issue. Any ideas on how I can adjust the rear derailleur to improve this? It just started happening and it's driving me crazy! Thanks so much.