A paper looks at the ultimate limits of a photon propulsion rocket. The maximum velocity for a photon propulsion rocket is just below the speed of light and is a function of the reduced Compton wavelength of the heaviest subatomic particles in the rocket. We are basically combining the relativistic rocket equation with Haug's new insight in the maximum velocity for anything with rest mass. An interesting new finding is that in order to accelerate any sub-atomic "fundamental" particle to its maximum velocity, the particle rocket basically needs two Planck masses of initial load. This might sound illogical until one understands that subatomic particles with different masses have different maximum velocities.