Basil shelf-life

If you use a lot of basil in your cooking you know it goes bad really quickly, even the bunches that come with roots attached in the grocery store. I've been growing my own basil this summer, and I've been experimenting with different ways to keep it fresh until I use it in my cooking, freeze it, or make pesto out of it. Cook's illustrated said that keeping it in the fridge in damp paper towels was the best way to store it, but I had pretty awful results with that method. The only thing that seems to keep them at least a week for me has been drying them with paper towels and then storing on the counter in a plastic air-tight container. I also store mint leaves this way (from my garden) and they seem to keep similarly fresh for longer.

I don't know if its because the basil is freshly picked versus already having travelled many miles to the supermarket, so let me know if you buy basil and it doesn't last using this method.