I will give you some very very sound advice pertaining to palms around pools.
1/ Ensure 1m away from concrete pool wall/foundation etc to CLOSEST EDGE OF MATURE TRUNK.
2/ Beware if planting clumping varieties or you may break rule 1 above.
3/ Ensure palms roots have space to grow in opposite direction to pool, not good if opposite direction to pool is brick fence or retaining wall.
4/ Do not plant monocarpic species.
5/ Most palms will grow 15m to 20m tall and all get some sort of berries, select slow growing varieties.
6/ Do not plant above or near pipes, they will break them.
There's a BIG FALACY about palm roots.
Watch this video 10.7mb WMV and 2.05mins
http://www.palmtreeservices.com.au/video/palmroots.wmv
Slow growing palms.
Spindle palm, Kentia Palm, Majestic palm, Triangle palm.
Small palm.
Cascade palm (chamaedorea atrovirens) can take full sun unlike parlour palm (chamaedorea elegans or bamboo palm).
Some alternative foliage stuff to add colour yet keep tropical, crotons, tri-coloured draecena, sacred bamboo (nandina domestic
nana), cordylines
Also dont overlook the value of some stunners where pool water overflow wont get them, Agave, Xanthorrhoea (grass trees) and cycads .
Tropical is a blending of both under story and canopy, but the hard part with palms is their height ... bangalows are a shocker, much skinnier than an Alexandra but just as tall.