  The basic system E of dyadic deontic logic proposed by {\AA}qvist offers a
simple solution to contrary-to-duty paradoxes and allows to represent norms
with exceptions. We investigate E from a proof-theoretical viewpoint. We
propose a hypersequent calculus with good properties, the most important of
which is cut-elimination, and the consequent subformula property. The calculus
is refined to obtain a decision procedure for E and an effective countermodel
computation in case of failure of proof search. Using the refined calculus, we
prove that validity in E is Co-NP and countermodels have polynomial size.
