  Given a Dirac subbundle and an isotropic subbundle of a Courant algebroid, we
provide a canonical method to obtain a new Dirac subbundle. When the original
Dirac subbundle is involutive (i.e., a Dirac structure) this construction has
interesting applications, for instance to Dirac's theory of constraints and to
the Marsden-Ratiu reduction in Poisson geometry.
