When the gauge instantons on the N = 2 string worldsheet are properly included in the sum over topologies, the breaking of SO(2,2) Lorentz symmetry in R2,2 is parametrized by a spacetime twistor containing the string coupling and theta angle. The resulting (tree-level) effective action for the open string is not Yang's but Leznov's cubic action for self-dual Yang-Mills in a light-cone gauge. In the closed case, Plebański's action for self-dual gravity gets modified analogously. In contrast to the N = 1 NSR string, picture-changing is not locally invertible, but produces a semi-infinite tower of massless physical states with ever-increasing spin, perhaps related to harmonic superspace. A truncation yields the two-field action of Chalmers and Siegel.