  The phenomenon of atomic population trapping in the Jaynes-Cummings Model is
analysed from a dressed-state point of view. A general condition for the
occurrence of partial or total trapping from an arbitrary, pure initial
atom-field state is obtained in the form of a bound to the variation of the
atomic inversion. More generally, it is found that in the presence of initial
atomic or atom-field coherence the population dynamics is governed not by the
field's initial photon distribution, but by a `weighted dressedness'
distribution characterising the joint atom-field state. In particular,
individual revivals in the inversion can be analytically described to good
approximation in terms of that distribution, even in the limit of large
population trapping. This result is obtained through a generalisation of the
Poisson Summation Formula method for analytical description of revivals
developed by Fleischhauer and Schleich [Phys. Rev. A {\bf 47}, 4258 (1993)].
