I had read thaqt you should not plant Redbud too close to Paving...
I too am in the midst of looking at differant trees and some I would consider for that situation because of your size, zone and water req are:

Flowering Pear or Plum (Maybe not spreading enough?)
Hong Kong Orchid
Trumpet Tree (tabebuia avellanedae)
Saucer Magnolia

I am not sure if these are non-invasive roots for around a Patio or if the canopy is suitable. I hope others can comment. I have just started some research myself. Also one thing that I also have learned from suggestions from people is to think about the style. (Tropical, Mediterranean, Cottage) That has been helping me pull things together better.
Just curious..Why don't you want to put in another Mimosa..I would have thought it looked nice in that location?

I would suggest a Crape Myrtle. Available in a variety of colors, and sizes, shapes etc. The leaves are not too dense, and also blossoms look attractive. In zone 16, my tree has just started growing leaves (this year has been cold though), and it has leaves until October. In zone 18 your season might be a bit more extended.

I vote for gleditsia. One variety leafs out in a beautiful shade of lime green, then the leaves darken. It is lacy like a mimosa, but small and not messy. I have one planted two feet from my flagstone patio (unfortunately, mine turned out to be the normal green variety).

Jacarandas have lacy leaves. Dappled shade. Beautiful blue blooms. But when they drop, they cause kind of a mess. Locust trees also have lacy leaves and give dappled shade. The problem is they are deciduous and in the fall drop their tiny yellow leaves everywhere. And their twisty seed pods. But that's okay. The redbud would not be good for a lawn because of too much water. Why not try the mimosa again; it does produce light shade. But I always prefer native trees to non-native, but unfortunately, most CA natives don't tolerate summer watering.

Thank you for all your responses. I have considered replacing with another mimosa but I am not sure why it died or for that matter if it is dead. It dropped all its leaves suddenly last Aug and I am still kind of waiting to see if new leaves appear this May. If they do I will keep it because it does work well in that site but I see no buds but the branches are still flexible. As for your suggestions, Saucer Magnolia is nice but does it get big enough? I don't know about the Trumpet tree or the Orchid tree I will check them out. Crape Myrtle is pretty but I already have some very nearby and I want something distinctive for this area. Jacarandas have an oder by hubby can't stand. Gleditsia I am not familar with but I am intrigued, I will check it out. Chitalpa is a beatiful tree and sounds like a good fit. Leaf litter is not a real problem it just gets mulched when we mow. The plum or pear tree gives me an idea, I have an apple tree out back that needs to be relocated it is only 2 years old do you think it could survive the move?

I wouldn't move a tree that is already growing. Unless you can get enough of the root ball. Summer is creeping up fast and it will be hot in no time flat. Relocating trees would be a problem. Try to relocate a tree or shrub when it goes dormant. Or just before it starts to bud. I don't like fruit trees as front shade trees. The drop fruit and people are always stealing them. I always prefer flowering trees over just green. A flowering cherry or pear is beautiful in the spring. I have a gorgeous double petaled japanese cherry in the front of my house and its coming into full bloom. The limbs get so loaded with flowers that they actually bend from the weight. Japanese magnolias are beautiful trees as well, producing gorgeous blooms in the very early spring and a nice shade tree in the summer. The deciduous magnolia doesn't get very big though. Not like the southern evergreen native magnolia (from the east coast). Here in So Cal, most shade trees are southern magnolias, canary island pine, jacarandas, eucalyptus and an occasional native cottonwood or walnut or sycamore. Also big leaf maple. Strange that your mimosa hasn't budded yet. Did you get a big chill this winter or too much rain? If the tree dropped its leaves last august, I would think it is dead. Some kind of root rot or something. Or a bad drought.

Another one that comes to mind is a Japanese maple. There is a variety called Bloodgood that has bright red leaves, that grows pretty tall, and then there is one that has green leaves with reddish borders, that has a nice fall color. Both are deciduous, and I am talking about the varieties that are tall; not the weeping, drooping kind. They come in standard forms, and you could prune them in a way that branches develop horizontally. I do not think they get 20ft tall though; I think more like 10-15 ft is my guess. In terms of growth I do not know how fast growing they are.
Hope this works for you!

A honey locust tree may be perfect for you. It is a deciduous tree with smaller leaves. It will provide dappled shade and will form a very nice canopy. When mature, the tree may be 30 feet high and fairly wide. You will have a very nice open area under the tree, perfect for planting hostas, caladiums, astilble and other shade loving plants. Also, when the leaves fall, it will take less work to rake up the smaller leaves.

As suggested, look at Japanese Maples. Lots of varieties that would do well with your dappled light and regular water. Bloodgood is nice but definitely slow growing.

Check out Chinese Pistache.