We examine the possibilities for constructing models with Dirac gaugino masses and unification of gauge couplings. We identify one promising model, and discuss to what extent it can have a "natural SUSY" spectrum. We then determine the low-energy constraints upon it, and propose a constrained set of boundary conditions at the unification scale. We describe the implementation of these boundary conditions in the spectrum-generator generator \SARAH and we perform a first exploration of the parameter space, specifically searching for points where the spectrum is relatively light. It is shown that the pattern of the masses of SUSY states is very different compared to any expectations from the constrained MSSM.

31 + 28 pages, 10 figures, 1 table