  We perform a detailed study of the consequences of isospin symmetry in the
Cabibbo favoured $D\to\Kbar\pi\pi$ decays. These processes are important for
precision testing of the Standard Model and for hadronic physics. Combining
isospin symmetry with a dispersive reconstruction theorem we derive a
representation in terms of one-variable functions which allows one to predict
all the $D\to\Kbar\pi\pi$ amplitudes given inputs from one $D^+$ mode and one
$D^0$ mode. From this, using dispersion relations and unitarity, we derive a
set of 6+6 Khuri-Treiman type integral equations which enable to take
three-body rescattering effects into account. A first test of this approach is
presented using experimental results on the $D^+\to K_S\piz\pip$ and the
$D^0\to K_S\pim\pip$ modes.
