The electronic charge and spin density at any point in space are reexpressed in terms of the expectation values of any member of a general class of global operators. For practical use with approximate wave functions, two particular choices of operator are made that should provide advantages for the difficult case of density evaluation at a nucleus. Formal properties of these operators are derived and discussed in detail. Certain serious difficulties known for the behavior of the global operator previously introduced by Hiller, Sucher, and Feinberg are ameliorated in the new formulations.