All solutions of the no-birefringence conditions for nonlinear electrodynamics are found. In addition to known Born-Infeld and Plebanski cases, we find a ``reverse Born-Infeld'' case, which has limit Plebanski, an ``extreme-Born-Infeld'' arises as Lagrangian constraint. Only weak-field limit, only extreme-Born Infeld avoid superluminal propagation in constant electromagnetic backgrounds, but al...