  It is well known that in q-matroids, axioms for independent spaces, bases,
and spanning spaces differ from the classical case of matroids, since the
straightforward q-analogue of the classical axioms does not give a q-matroid.
For this reason, a fourth axiom has been proposed. In this paper we show how we
can describe these spaces with only three axioms, providing two alternative
ways to do that. As an application, we show direct cryptomorphisms between
independent spaces and circuits and between independent spaces and bases.
