  Modern hadron-spectroscopy experiments such as COMPASS collect data samples
of unprecedented size, so that novel analysis techniques become possible and
necessary. One such technique is the freed-isobar partial-wave analysis (PWA).
In this approach, fixed parametrizations for the amplitudes of intermediate
states commonly modeled using Breit-Wigner shapes are replaced by sets of
step-like functions that are determined from the data. This approach not only
reduces the model dependence of partial-wave analyses, but also allows us to
study the amplitudes of the intermediate states and their dependence on the
parent system.
  We will also present results of a freed-isobar PWA performed on the large
data set on diffractive production of three charged pions collected by the
COMPASS experiment, which consists of $46\times10^6$ exclusive events. We will
focus on results for the wave with spin-exotic quantum numbers $J^{PC}=1^{-+}$,
in particular on its decay into $\rho(770)\pi$. Here, the freed-isobar PWA
method provides insight into the interplay of three- and two-particle dynamics
and confirms the decay of the spin-exotic $\pi_1(1600)$ resonance to
$\rho(770)\pi$ in a model-independent way.
