  We construct a Dirac equation that is consistent with one of the
recently-proposed schemes for a "doubly-special relativity", a relativity with
both an observer-independent velocity scale (still naturally identified with
the speed-of-light constant) and an observer-independent length/momentum scale
(possibly given by the Planck length/momentum). We find that the introduction
of the second observer-independent scale only induces a mild deformation of the
structure of Dirac spinors. We also show that our modified Dirac equation
naturally arises in constructing a Dirac equation in the kappa-Minkowski
noncommutative spacetime. Previous, more heuristic, studies had already argued
for a possible role of doubly-special relativity in kappa-Minkowski, but
remained vague on the nature of the consistency requirements that should be
implemented in order to assure the observer-independence of the two scales. We
find that a key role is played by the choice of a differential calculus in
kappa-Minkowski. A much-studied choice of the differential calculus does lead
to our doubly-special relativity Dirac equation, but a different scenario is
encountered for another popular choice of differential calculus.
