  Stationary solutions to the equations of non-linear diffusive shock
acceleration play a fundamental role in the theory of cosmic-ray acceleration.
Their existence usually requires that a fraction of the accelerated particles
be allowed to escape from the system. Because the scattering mean-free-path is
thought to be an increasing function of energy, this condition is
conventionally implemented as an upper cut-off in energy space -- particles are
then permitted to escape from any part of the system, once their energy exceeds
this limit. However, because accelerated particles are responsible for
substantial amplification of the ambient magnetic field in a region upstream of
the shock front, we examine an alternative approach in which particles escape
over a spatial boundary. We use a simple iterative scheme that constructs
stationary numerical solutions to the coupled kinetic and hydrodynamic
equations. For parameters appropriate for supernova remnants, we find
stationary solutions with efficient acceleration when the escape boundary is
placed at the point where growth and advection of strongly driven non-resonant
waves are in balance. We also present the energy dependence of the distribution
function close to the energy where it cuts off - a diagnostic that is in
principle accessible to observation.
