To make the grapefruit segments: Cut both ends off the grapefruits and stand the grapefruits on a cutting board. With a paring knife, trim off the peel and white pith from the grapefruits, removing as little of the grapefruit flesh as possible. Working over a bowl, cut the segments free of the membrane, letting the segments drop into the bowl. After you've cut all the segments, squeeze all the juice out of the membranes into the bowl. Refrigerate the segments in the juice until needed, up to 2 hours.

Just before serving, cut the avocados in half, remove the pit and peel the halves. Slice each half lengthwise into 6 thin slices. Drain the grapefruit and reserve the juice (for the salad, if using, or as a treat for the cook). Add the avocado to the grapefruit along with the olives and lime juice. Toss gently to mix, while adding just enough olive oil to coat the avocado. Season, to taste, with salt and pepper and toss again. If you like, use a little of the reserved grapefruit juice to add a little zing to the salad.