Inspired by work of Masser and Zannier for torsion specializations of points on the Legendre elliptic curve, Baker and DeMarco proved that if v,w are two points in C, then there are at most finitely many t in C such that v and w are both preperiodic for the polynomial x^2 + t, unless of course v equals plus or minus w.  Here we prove a two-dimensional version of this result, namely that if v, w, and z are distinct complex numbers, then the set of parameters (a,b) such that v,w, and z are all preperiodic under f(x) = x^3 + ax + b cannot be Zariski dense in the affine plane. This represents joint work with Liang-Chung Hsia and Dragos Ghioca.