The generalization of the Satake–Baily–Borel compactification to arbitrary period maps has been reduced to an extension problem on certain “neighborhoods at infinity.” Extension problems of this type require that the neighborhood be pseudoconvex. The purpose of this note is to establish the desired pseudoconvexity in one relatively simple, but non-trivial, example: codimension one degenerations of a period map of weight two Hodge structures with \(p_g=2\) .