  We consider solutions of the 2-d compressible Euler equations that are steady
and self-similar. They arise naturally at interaction points in genuinely
multi-dimensional flow. We characterize the possible solutions in the class of
flows L^\infty-close to a constant supersonic background. As a special case we
prove that solutions of 1-d Riemann problems are unique in the class of small
L^\infty functions. We also show that solutions of the backward-in-time Riemann
problem are necessarily BV.
