There are now in the literature two proposals of relativity theories with observer-independent scales of both velocity and length/mass: one, which we here call “DSR1”, proposed by Amelino-Camelia in gr-qc/0012051,hep-th/0012238 and one, which we here call “DSR2”, proposed by Magueijo and Smolin in hep-th/0112090. We argue that a key aspect of such theories are the kinematical conditions for par...