The possibility of exciting microwave oscillations in a nanomagnet by a spin-polarized current, as predicted by Slonczewski and Berger, has recently been demonstrated. This observation opens important prospects of applications in radiofrequency components. However, some unresolved inconsistencies are found when interpreting the magnetization dynamics within the coherent spin-torque model. In some cases, the telegraph noise caused by spin-currents could not be quantitatively described by that model. This has led to controversy about the need for an effective magnetic temperature model. Here we interpret the experimental results of Kiselev et al. using micromagnetic simulations. We point out the key role played by incoherent spin-wave excitation due to spin-transfer torque. The incoherence is caused by spatial inhomogeneities in local fields generating distributions of local precession frequencies. We observe telegraph noise with gigahertz frequencies at zero temperature. This is a consequence of the chaotic dynamics and is associated with transitions between attraction wells in phase space.