We find the radius of Ma-Minda starlikeness of normalised analytic functions of the form (z) = z(f ′ (z)) α , α > 0 where f is in the class CV[A, B] of Janowski convex functions and (z) = z(z f ′ (z)/ f (z)) α , α > 0 where f is in the class CV ′ defined. As particular cases, we obtain criteria for these functions to belong to certain Ma-Minda classes.