Fwd: Natural understory beneath Olives

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I have a grove of young olives in my garden, and by

next year they should be tall enough to walk beneath

(they've grown fast!).  The understory is now mostly

Cistus ladanifer and Lavandula stoechas 'Otto Quast'. 

But, as the trees are now casting some shade, the

Cistus are beginning to get loose, and the lavenders

are looking odd, out of place in the partial shade.

What grows beneath wild olives, or beneath an

abandoned olive orchard,  in southern Europe?

As I live in southern California, I'm leaning toward

natives as an understory: Ceanothus 'Frosty Blue' has

been an ok background shrub, though not as floriferous

as in sun, and this past fall I've planted some

Arctostaphylos 'Bert Johnson' and Carpenteria

californica, so we'll see how they do.

Is a more herbaceous groundcover more appropriate? 

Maybe Fragaria chiloensis and Heuchera maxima

cultivars?

Thanks for any advice!

-Ben Wiswall