  We investigate how deformations of special relativity in momentum space can
be extended to position space in a consistent way, such that the dimensionless
contraction between wave-vector and coordinate-vector remains invariant. By
using a parametrization in terms of an energy dependent speed of light, and an
energy dependent Planck's constant, we are able to formulate simple
requirements that completely determine the active transformations in position
space. These deviate from the standard transformations for large velocities of
the observed object. Some examples are discussed, and it is shown how the
relativistic mass gain of a massive particle is affected. We finally study the
construction of passive Lorentz-transformations.
