  The Conditional Probability Interpretation (CPI), first introduced by Page
and Wootters, is reviewed and refined. It is argued that in it's refined form
the CPI is capable of answering various past criticisms. In particular,
questions involving more than one clock time are described in detail, resolving
the problems raised in Kuchar's ``reduction ad absurdum''. In the case of
Parametrized Particle Dynamics, conventional quantum mechanics is recovered in
the ideal clock limit. When E=0 is among the continuous spectrum of the
Hamiltonian, the induced inner product is used to construct the physical
Hilbert space $\clh_{\rm ph}$ from the generalized eigenvectors in (the
topological dual of) $\clh_{\rm aux}$. This allows the CPI to be applied to
these `continuous-spectrum' cases in a more rigorous fashion than that
described previously. The discrete spectrum case is also treated.
