  We study the constraints imposed on the population and phase relaxation rates
by the physical requirement of completely positive evolution for open N-level
systems. The Lindblad operators that govern the evolution of the system are
expressed in terms of observable relaxation rates, explicit formulas for the
decoherence rates due to population relaxation are derived, and it is shown
that there are additional, non-trivial constraints on the pure dephasing rates
for N>2. Explicit experimentally testable inequality constraints for the
decoherence rates are derived for three and four-level systems, and the
implications of the results are discussed for generic ladder-, Lambda- and
V-systems, and transitions between degenerate energy levels.
