  Let S be a smooth cubic surface defined over a field K. As observed by Segre
and Manin, there is a secant and tangent process on S that generates new
K-rational points from old. It is natural to ask for the size of a minimal
generating set for S(K). In a recent paper, for fields K with at least 13
elements, Siksek showed that if S contains a skew pair of K-lines then S(K) can
be generated from one point. In this paper we prove the corresponding version
of this result for fields K having at least 4 elements, and slightly milder
results for #K=2 or 3.
