  We prove that for certain families of semi-algebraic convex bodies in 3
dimensions, the convex hull of $n$ disjoint bodies has $O(n\lambda_s(n))$
features, where $s$ is a constant depending on the family: $\lambda_s(n)$ is
the maximum length of order-$s$ Davenport-Schinzel sequences with $n$ letters.
The argument is based on an apparently new idea of `compact families' of convex
bodies or discs, and of `crossing content' of disc intersections.
