GARDENING : Shade for the Patio : Landscape designers suggest perfect trees for decks and suburban yards: not too big, not too particular about climate, not too messy.

You’ve just sent the last check to the contractor; your new deck or patio is complete, almost. Except that every time you sit on it, the Valley sun blasts you back to the air conditioner.

You need a patio tree. A neat tree, not too big, guaranteed to give shade, whose roots will not push up the flagstones or warp the wood decking. While our first inclination may be to find an elm or a cedar just like the ones in our parents’ neighborhood in Chicago or Santa Cruz, we must quell the impulse. Street trees, while definitely shady, will overwhelm a back yard and make an average-size house look like it’s huddling in fear.

Smaller trees are not just wimpy compromises. The peppermint willow, Agonis flexuosa , though dainty and delicate looking, has a smell that is “so wonderful when you crush the leaf,” says Santa Monica-based landscape designer Mary Effron. “It’s heavenly. And it has a weeping willow look to it, but it’s drought-tolerant.”

From Australia, the evergreen peppermint willow has olive-colored leaves, reddish bark, small white flowers in June and a broad crown that reaches about 30 feet. Its drawback: It will die back to the ground if winter temperatures get down to 25 degrees Fahrenheit.

One of the most beautiful trees anywhere is the purple leaf plum, Prunus cerasifera. Although frequently upright in their youth, these trees spread out over time. Their beautiful mahogany leaf color looks spectacular against a pastel house and over silver plants such as artemisia and santolina. The “Krauter Vesuvius” cultivar is small, reaching 18 feet with a 12-foot spread, with dark purple leaves and pink flowers. Other cultivars offer different sizes and variations in flower and leaf color. And there are no climatological worries with prunus; it can take any winter the Valley can muster.

Nor is it fussy about soil, and while it is not drought-tolerant, it needs only a good, deep weekly drink to get it through the summer. Drawback (to some): It is deciduous, so its leaves will drop in winter. This is really a benefit in disguise, because it gives us seasonal change, and it lets winter sun through the branches to warm us when we need warming. Besides, leaf raking is good for the soul and the arms.

While we’re mentally raking leaves, we might also consider lagerstroemia , or crape myrtle, famous for its adaptability to the Valley climate--it loves hot summers. Also for its abundant flowers that cover the trees in late summer and, a nice bonus, for its fall leaf color (yellow to red). There are now three hybrid cultivars that are mildew resistant: “Muskogee,” with lavender flowers; “Natchez,” white; and “Tuscarora,” coral pink. Quick growing to 25 feet, lagerstroemias do not spread out until they are about 8 years old, but they bloom like crazy from an early age.

Of the dozens of evergreen patio trees that thrive in the Valley, Doug Henderson at Valley Crest Tree Service, a wholesale-only business that supplies many trees to Southern California nurseries, suggests the weeping mayten tree, or Maytenus boaria , another small-scale weeping tree, this with deep green leaves; the oleander tree, a pruned standard of the freeway favorite--”if you like the flower”; and dwarf magnolias, with full-size flowers. The dwarfs reach about 20 feet instead of 80.

Tarzana-based designer Mark David Levine also prefers the mayten--”a really beautiful tree”--plus the evergreen pineapple guava, Feijoa sellowiana , a handsome gray-leafed bushy tree with delicious fruit.

Finally, the perfect evergreen patio tree: Perfect if you have a large yard and a Spanish-style house. Perfect if you don’t mind continuous litter and if you enjoy a sense of history. The California pepper tree, Schinus molle , with its delicate leaves drooping over a stone bench or a stucco wall, evokes another time, when Indians and dons and friars, crushed by the summer heat, would sit under just such a pepper tree and feel revived.

It has the same effect today.