What zone are you in? Bananas are good and have cold hardy species available as well. There's a great tropical gardening forum that might give you some good suggestions. Haven't been over there in a bit, but I remember some pool owners.

Here is a link that might be useful: Tropical Gardening

Crepe mytles are beautiful specimines but I would never plant one hear a pool. Everything has litter, but crepes are by far the worst offender. If it's not the blooms, it's the leaves and seed heads.
We are here in the DFW area and it took some time researching what would work for us in our climate, the desired area (pool area) and that could stand our very alkaline soil and high sodium content well.
This photo is summer 2010 and everything was planted that spring.
Behind the grotto and to each side is heavenly bamboo nandina. It will grow tall, 5-6 ft. Has minimal litter. Excellent fall and spring color.
One each side of the grotto, is Double Knock Out Roses in red. It is really not a red "red" and the blooms fade to shades of pink. It is a profuse bloomer spring-frost. Unless you want them to reach mature height (around 4x4),I cut them back to about 18-24 inches (we have older ones out front). These roses have posed very minimal litter as well when the blooms fall.
Then we suppliment with annuals. Pink Zinnias flank the rock border. Zinnias love sun, tolerate drought and spread. The only time these were aweful was I pulled them too late, after they were dead and brown, and stuff went everywhere.
In with the pink Zinnias is white periwinkles.
following the fence line, behind the rock ledges, is orange canna with bright green leaves. It contrasts with the dark green of the roses.
Good luck in your landscaping!
Here are some pics I find that might help. (The one plant sticking out everywhere is a bouganvilla. It was a hanging basket but I planted it. As soon as I did, it never bloomed again, but grew huge. It also has horrible thorns. The Canna have not come up quite yet.