Every probability measure μ \mu on the circle group generates a function f that is starlike univalent on the open unit disc Δ \Delta . In this note the relationship between ( c n ) ({c_n}) , the Fourier-Stieltjes coefficients of μ \mu , and ( a n ) ({a_n}) , the Taylor coefficients of f, is examined. A number of theroems are presented which indicate (possibly in the presence of fairly mild restrictions) that the sequences ( c n ) ({c_n}) and ( n a n ) (n{a_n}) behave similarly. For example, it is shown that if f ( Δ ) f(\Delta ) is finite, then ( c n ) ({c_n}) converges to zero if, and only if, ( n a n ) (n{a_n}) converges to zero, thereby completing a result of Pommerenke.