A rotated odometer is an infinite interval exchange transformation (IIET) obtained by pre-
composing the von Neumann-Kakutani map with an exchange of a finite number of intervals of equal
length. Such IIETs model the first return maps of flows on certain translation surfaces with wild singular-
ities. In this talk, we consider the ergodic properties (i.e. recurrence, discrepancy, diffusion coefficient and ergodicity) of skew-products over rotated odometers. Our main tools are theory of essential values, and the symbolic dynamical representations of the rotated odometers. Joint work with Henk Bruin (University of Vienna).