  We provide a novel perspective on "regularity" as a property of
representations of the Weyl algebra. In Part I, we critiqued a proposal by
Halvorson [2004, "Complementarity of representations in quantum mechanics",
Studies in History and Philosophy of Modern Physics 35(1), pp. 45--56], who
advocates for the use of the non-regular "position" and "momentum"
representations of the Weyl algebra. Halvorson argues that the existence of
these non-regular representations demonstrates that a quantum mechanical
particle can have definite values for position or momentum, contrary to a
widespread view. In this sequel, we propose a justification for focusing on
regular representations, pace Halvorson, by drawing on algebraic methods.
