  First-class constraints constitute a potential obstacle to the computation of
a Poisson bracket in Dirac's theory of constrained Hamiltonian systems. Using
the pseudoinverse instead of the inverse of the matrix defined by the Poisson
brackets between the constraints, we show that a Dirac-Poisson bracket can be
constructed, even if it corresponds to an incomplete reduction of the original
Hamiltonian system. The uniqueness of Dirac brackets is discussed.
