  There are known obstructions to a full quantization in the spirit of Dirac's
approach, the most known being the Groenewold-van Hove no-go result. We show,
following a suggestion of S. K. Kauffmann, that it is possible to construct a
well-defined quantization procedure by weakening the usual requirement that
commutators should correspond to Poisson brackets. The weaker requirement
consists in demanding that this correspondence should only hold for Hamiltonian
functions of the type T(p)+V(q). This reformulation leads to a non-injective
quantization of all observables which, when restricted to polynomials, is the
rule proposed by Born and Jordan in the early days of quantum mechanics.
