An analysis of core phase travel times is performed in order to estimate the relative contributions of heterogeneities and anisotropy and their distribution inside the inner core. A stochastic analysis performed on the equatorial paths, which are poorly sensitive to anisotropy, indicates that the inner core exhibits a heterogeneity level smaller than 0.3% at all depths on scale lengths larger than 200 km. This result, extended to all path orientations, suggests a predominant effect of the anisotropy on travel times anomalies. A simultaneous inversion of absolute and differential core phase travel times for any path orientation favours a simple inner core model in which a large, homogeneous structure with 3% uniform anisotropy is asymmetrically surrounded by a homogeneous isotropic layer with a thickness of 100--200 km on the western hemisphere, increasing to 400 km over a large part of the eastern hemisphere. ¿ 2000 American Geophysical Union