  Wave functions describing quantum toboggans with two branch points (QT2) are
defined along complex contours of coordinates which spiral around these branch
points. The classification of QT2 is found in terms of certain ``winding
descriptors" $\varrho$. A mapping $x^{(\varrho)}(s) \to y^{(0)}(s)$ is then
presented which rectifies the contours for a subset of the simplest
$\varrho=\varrho_0$.
