We propose a practical parametrization for the line shapes of near-threshold states compatible with all requirements of unitarity and analyticity. The coupled-channel system underlying the proposed parametrization includes bare poles and an arbitrary number of elastic and inelastic channels treated fully nonperturbatively. The resulting formulas are general enough to be used for a simultaneous analysis of the data in all available production and decay channels of the (system of) state(s) under consideration for a quite wide class of reactions. As an example, we fit the experimental data currently available for several decay channels for the charged Z super((')) sub(b) states in the spectrum of bottomonia and find a good overall description of the data. We find the present data to be consistent with the Z sub(b)(10610) as a virtual state and with the Z sub(b)(10650) as a resonance, both residing very close to the BB* and B*B* threshold, respectively.