  When deriving exact generalized master equations for the evolution of a
reduced set of degrees of freedom, one is free to choose what quantities are
relevant by specifying projection operators. However, obtaining a reduced
description does not always need to be achieved through projections--one can
also use conservation laws for this purpose. Such an operation should be
considered as distinct from any kind of projection; that is, projection onto a
single observable yields a different form of master equation compared to that
resulting from a projection followed by the application of a constraint. We
give a simple example to show this point and give relationships that the
different memory kernels must satisfy to yield the same dynamics.
