Ann, I use self-watering pots as well as flower-box planters... were the ones you were looking at the types with a hole near the bottom where you can add water? That will also act as an "overflow" if the plant gets overwatered from the top, such as with excess rain. My plants do great in those types of containers; in fact, the flower boxes that I hang on our deck railing on the south side of our house are the first thing that I've actually been able to grow flowers in there during the summer -- the midsummer sun directly from the south gets pretty brutal even up north here!
