We present the spectrum of stationary black hole solutions associated with the first non-trivial member of the Dym family of boundary conditions. The analysis combines the holonomy conditions provided by the Chern-Simons formulation of AdS3 gravity with the periodic solutions of the stationary Dym equation. The resulting spacetimes are characterized by two positive real parameters, two positive integers, and a relative phase, generically describing stationary, non-axisymmetric black holes.