Sharp coefficient inequalities are given for f normalised and analytic in z ∈ D = {z : |z| < 1}, and satisfying arg z f (z) f (z) − α < πβ 2 (z ∈ D) for α ∈ [0, 1) and β ∈ (0, 1]. The results generalise and unify known inequalities for starlike functions in a half-plane, and strongly starlike functions.