the Bottle palm and Dypsis would work well, i dont know much about cherry palms ?psuedophoenix i think they get past 20'. others to consider would be Pygmy date palm, dypsis lutescens, Spindle palm. or if you want some color the sealing wax palm and flamethrower palm will not grow over 20'.
just out of curiosity do you know what palm is planted there now?

Sorry, I forget the name. It is a pinnate but not anything as common as queen or foxtail. Maybe adonidia or a similar palm?

you live in 10a Florida or 10a California? If the latter, don't bother with Hyophorbe laugenicaulis (bottle palms) as they will not do well for you (too cold for them)... in Florida, you might be OK with that one. Pseudophoenix are so slow that in California you will not live long enough to see one grow over 20' (I don't think there is one that tall in this entire state, and there won't be for another 10-20 years most likely). Florida is different, though, and those palms will grow over 20' there, in less than 20 years even. You have to live in florida if you have an Adonidia as they don't survive in California, either (except exceptional 10b climate areas.. .even then, they survive.. never get as tall as 20' though). You want a suckering palm or a solitary? Because most of those Dypsis sp. will sucker... Flamethrowers (Chambeyronias) will easily grow over 20' and we have many in California that are way over 20' now... in Florida they do even better so I would not recommend one of those (plus they don't like full sun in most climates). What is your sun exposure situation? Phoenix roebelleniis are super common, but they sound like they will fit your situation pretty well. Dypsis lutescens and baronii can grow over 20' (though baronii rarely do).

Hi
There are several posts on the florida forum with pix on this ?? I suggested some of the rarer types since you have the advantage of a planter as well as wind protection.
Some more suggestions would be to skip the palm family for larger Bromeliads,Aroids, Cycads?? gary

Hi,lzrddr,

I'm in Florida zone 10a, Palm Beach County. The exposure is direct sun on my patio, so, although the screen gives some protection, I can't have something that wants part shade or will burn in direct sun.

Gary, yes, I posted both places, thinking it would increase the potential suggestions! My husband is fairly set on some type of palm (he's an engineer, what can I say), but I am definitely thinking of some of the large Achmeas for accent plants around them.

Some suggestions:

Pinnate leaves

Dictyosperma album var. furfuracea
Hyophorbe lagenicaulis (bottle)
Pseudophoenix sargentii (buccaneer)
Syagrus coronata
Sygrus schizophylla

Palmate leaves

Coccothrinax miraguama
Coccothrinax readii
Rhapis multifida
Thrinax radiata
Leucothrinax morrisii

These should stay small or grow so slowly that they'll be small for a long while. I left out palms with thorns or spines.

Hope this helps.

Thanks, Steve and all who posted with advice. I must ponder...

Don't know much about palms but I came across an interesting article in the Tampa Bay Times (old St Pete Times) about them. Edible fruit off a palm....

Most palm seeds look very much alike. The palm, (pindo or jelly palm) has silvery grey, feather type (pinnate) fronds with hooked thorns at the base and the fronds arch backward. The trunk is solitary and stout with front bases (boots) still attached. The fruit is round, like a jawbreaker, orange and quite tasty to eat. It is very cold hardy and slow grower with trunks not much over 10 � 15 feet in the Tampa Bay area.
A second choice is queen palm..�syagrus romanzoffiana�, a single clean trunk (no boots) gray in color. The fronds are feather type (pinnate) with no thorns at the base. Most of the fruits are oblong like an olive instead of round, orange in color, like the pindo. The orange flesh is edible, very sweet and fibrous, but is not as tasty as the pindo. It is one of the fastest growing palms for the Bay area and is hardy.

This may not be what you were looking for but I thought I'd add to what others were contributing.

I agree with the suggestion to look at Cycads. Many of them are relatively hardy and most grow very slow.

Syagrus romanzoffiana grows quite tall and is a pretty fast grower.