Help on establishing a new lawn

Greetings. I have been looking for answers on my gardening questions, and although I'm close, there's one huge question I have left to answer. First, the details.
I live in Burbank, CA (semi-arid, lost of sandy soil, tons of sun, not much rain, but not a desert).
I have a front yard that is relatively small (2 areas 10' x 15') with 3 large well established trees (one is a maple, the other two I'm not sure). When I moved in 3 years ago, the yard was totally overgrown with crab grass. The owner seemed to think this was a "lawn".
I want to replant the whole thing with something fairly hearty and drought tolerant, but at least a grass and not a weed. The plan was to kill with round up (done), and remove the old dead crab grass, and plant new grass.
However, the step I'm on is removal of crab grass and prepping the soil, which in normal circumstances requires tilling (which almost everyone says "NO TILLING AROUND TREES").
My question is.... what then? How do you prep soil for grass? I understand grass and trees do compete for water, etc, but my yard is so small that if I leave room around the trees, I just have a brown front yard!
Is there a good alternative to tilling around trees? Just how bad is it to till? Should I kiss my shade trees goodbye?
If this question has been answered already (I searched google already) I won't be offended by links that might help point me in the right direction.
Thanks,
P
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If your maples are mature or maturing, grass will be difficult to grow under them. (They usually have very shallow root systems that out compete grass - plus dense shade). Maybe, at least under their driplines, you should consider a somewhat drought tolerant ground cover, such as vinca, or pachysandra, or else put a barrier there and simply put bark under the trees, and plant grass to the outside of the dripline.

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