  Numerous quarkonium(like) states lying near $S$-wave thresholds are observed
experimentally. We propose a self-consistent approach to these near-threshold
states compatible with unitarity and analyticity. The underlying
coupled-channel system includes a bare pole and an arbitrary number of elastic
and inelastic channels treated fully nonperturbatively. The resulting
analytical parametrization is ideally suited for a combined analysis of the
data available in various channels that is exemplified by an excellent overall
description of the data for the charged $Z_b(10610)$ and $Z_b(10650)$ states.
