  We resume the study of the Cabibbo-favored charmed-meson decays $D^+ \to
\bar{K} \pi \pi^+$ in a dispersive framework that satisfies unitarity,
analyticity, and crossing symmetry by construction. The formalism explicitly
describes the strong final-state interactions between all three decay products
and relies on pion-pion and pion-kaon phase shift input. For the first time, we
show that the $D^+ \to K_S \pi^0 \pi^+$ Dalitz plot obtained by the BESIII
collaboration as well as the $D^+ \to K^- \pi^+ \pi^+$ Dalitz plot data by CLEO
and FOCUS can be described consistently, exploiting the isospin relation
between the two coupled decay channels that provides better constraints on the
subtraction constants.
