  We develop a quantization method, that we name decomposable Weyl
quantization, which ensures that the constants of motion of a prescribed finite
set of Hamiltonians are preserved by the quantization.
  Our method is based on a structural analogy between the notions of reduction
of the classical phase space and diagonalization of selfadjoint operators. We
obtain the spectral decomposition of the emerging quantum constants of motion
directly from the quantization process.
  If a specific quantization is given, we expect that it preserves constants of
motion exactly when it coincides with decomposable Weyl quantization on the
algebra of constants of motion. We obtain a characterization of when such
property holds in terms of the Wigner transforms involved. We also explain how
our construction can be applied to spectral theory.
  Moreover, we discuss how our method opens up new perspectives in formal
deformation quantization and geometric quantization.
