It's strange that you don't want to be cleaning your pool of leaves. How about a Japanes maple, grafted, but I don't know how they would mix with palms, because here in Charlotte, palms get hit. Why not some perennial groundcovers that bloom a good part of the summer, like coreopsis, you have at least 3 different colors to choose from and they'll mix with liriope.

Here is a link that might be useful: Propagating Perennials

i think you're referring to the jelly palm. Not sure of the botanic, but should be easy enough to google. They are a little more touchy than windmill palms, but are hardy for z 8. I think they're much prettier myself!

I'd suggest planting some New Zealand Flax as accent to the thinner grasses mentioned. The cordyline grows like a yucca, with a central stalk, so it needs to be set apart as a focal point. It is too similar in leaf shape, but not similar enough in growth form to properly accent the grasses, I think. ;)
Assuming your area looks similar to the picture I have made in my head, I think it would look great to have a small water garden where the tree is supposed to go. You could plant giant papyrus for height and to tie in with the othwer grasses of the border, and plant water lilies and pickerel weed for a three step visual focal point.
These are just opinions, of course. I would also offer the idea of finding a large specimen of croton to pot/plant where you wanted the accent tree. You can find one at 2.5/3.5ft for about $30. It will give you your tropical look with out fruiting or dropping leaves. Bear in mind that it is NOT hardy in zone eight, so it could be planted as an annual, or potted and brought inside before the frost.
---Keith

Washingtonia robusta is hardy to 18 degrees. Some people call it a mexican fan palm and they can make a nice sized tree.

Phoenix xanariensis will take the 20's. It is the true Canary Island Date Palm. Both are popular in the southern parts of Texas where I grew up.

Both are nice trees

I think the jelly palm genus is Buhtia or Bhutia or something similar.

I'd plant Hardy Banana if you want tropical - Musa basjoo (Japanese fiber banana). Dies back to about a foot or so above the ground but comes back strong each year. They eventually make a big clump. No special treatment required except lots of food early in the spring. They don't make edible bananas.

I can tell you what NOT to plant - any of the ornamental grasses with wide blades. Blades being the operative word. Their leaves are like razor blades and not something you'd want to rub against while wearing a swimming suit (or not wearing a swimming suit, depending on the privacy of your pool). This includes most of the variegated ones and the tall sugar cane ones (purple or green forms). Also, avoid the tropical looking Tetrapanax (Rice paper plant). They give off a powdery fiber stuff that some people are very senistive to, and it can make you itch. You could go with Fatsia, looks tropical but likes shade more than full sun. All choices need to be checked for chlorine tolerance - some plants can't stand even the odor of chlorine.

Thanks so much for the responses so far. Re: Japanese maple, I love those, and I agree they don't really look tropical. I may just get one anyway. I figure the small leaves they have wouldn't cause too much of a problem with the pool (would actually be about 12 feet from the water's edge.)

I googled all the palms suggested here, and they all grow too tall or big around. I need something compact. The Canary Palm wouldn't work, since it usually gets into the teens a few times in the winter here. I think the Banana would eventually be too big also.

Re: the grasses next to the pool, really they would be about 7-10 feet away from the edge. We have several feet of pool deck, then a row of liriope, then a couple of feet of pea gravel. We want to discourage walking on the pea gravel, so I think we will be OK with the ornamental grasses there.

Any more suggestions on the small tree?

Pineapple Guava (Feijoa somethingorother)

Any of the perennial hibiscus

Loquat (does eventually get big)

Well, I am breaking one of my "rules", but if you PROMISE to cut it to the ground annually, and kill it off whenever you put the house on the market, a Paulownia cut to the ground annually has really big, tropical looking leaves, and will stay pretty small - under 10' anyway. You will get no flowers, but that's all to the good, since it then can't exercise its invasive tendencies. Since I don't know where you live, it might do that anyway if it gets cold enough in the winters.

Cotinus, smoke tree might work, and has cultivars with green, red/purple or lime-green leaves. Cut to the ground annually, it should stay small enough, or, take out a third of the stems annually, and it should stay fairly small.

While not a tree, cannas are tropical looking, as are elephant ears and caladiums. What about, at a suitable distance from the pool, one of the large aloes?

Thanks so much for the replies! I would love to do caladiums or elephant ears in the location next to my raised deck, but my back yard gets about 8 hours of full-blazing sun in the summer.

I think I've decided to just put a trellis there, and plant one or two roses.

Another thing that looks amazingly tropical and is actually annual here would be a papaya. You can start them from supermarket seed in the winter then plant out a seedling which will get to 6-10' by the end of the summer! Wonderful foliage, and not too wide- single trunk. At the farmer's market i saw someone putting them in the middle of color baskets. Didn't get a chance to stop & ask if they had them separate- probably not. But it's nice to see them being incorporated. Castor bean could be used similarly, and in act looks similar, but more branchy- and very very poisonous if you have little kids. Both those would love sun. I don't think the chinese fiber banana gets anywhere near as tall as regular bananas, fyi- and they have a more fan like profile. Very cool. Also, you could plant the caladiums & such in the shade cast by a small tree. Another small tree/ bush that looks very tropical is hardy tapioca. It will come back each year. EE's can handle the sun if they're kept moist enough. Nothing looks more tropical to me.

If you end up with a trellis, rather than doing roses, you could do more tropical looking vines on it. Mina lobata, the big blue thunbergia, passionflower and mandevilla all pop out at me as good options.