In the framework of the Weyl-Hörmander calculus, under a condition of "geodesic temperance", pseudodifferential operators can be characterized by the boundedness of their iterated commutators. As a corollary, functions of pseudodifferential operators are themselves pseudodifferential. Sufficient conditions are given for the geodesic temperance. In particular, it is valid in the Beals-Fefferman calculus.