Summary: As has been shown by S. Watanabe and S. H. Strogatz (WS) [Phys. Rev. Lett. 70, No. 16, 2391–2394 (1993; Zbl 1063.34505)], a population of identical phase oscillators, sine-coupled to a common field, is a partially integrable system: for any ensemble size its dynamics reduce to equations for three collective variables. Here we develop a perturbation approach for weakly nonidentical ensembles. We calculate corrections to the WS dynamics for two types of perturbations: those due to a distribution of natural frequencies and of forcing terms, and those due to small white noise. We demonstrate that in both cases, the complex mean field for which the dynamical equations are written is close to the Kuramoto order parameter, up to the leading order in the perturbation. This supports the validity of the dynamical reduction suggested by E. Ott et al. [Chaos 18, No. 3, 037115, 9 p. (2008; Zbl 1309.34060)] for weakly inhomogeneous populations.