New stationary solutions of four-dimensional dilaton-axion gravity are presented, which correspond to the charged Taub-NUT and Israel-Wilson-Perjés (IWP) solutions of Einstein-Maxwell theory. The charged axion-dilaton Taub-NUT solutions are shown to have a number of interesting properties: (i) manifest SL(2,R) symmetry; (ii) an infinite throat in an extremal limit; (iii) the throat limit coincides with an exact CFT construction. The IWP solutions are shown to admit supersymmetric Killing spinors, when embedded in d=4,N=4 supergravity. This poses a problem for the interpretation of supersymmetric rotating solutions as physical ground states. In the context of 10-dimensional geometry, we show that dimensionally lifted versions of the IWP solutions are dual to certain gravitational waves in string theory.