Let π» be the open unit disc, let v:π»β(0,β) be a typical weight, and let Hvβ be the corresponding weighted Banach space consisting of analytic functions f on π» such that . We call Hvβ a typical-growth space. For Ο a holomorphic self-map of π», let CΟ denote the composition operator induced by Ο. We say that CΟ is a bellwether for boundedness of composition operators on typical-growth spaces if for each typical weight v, CΟ acts boundedly on Hvβ only if all composition operators act boundedly on Hvβ. We show that a sufficient condition for CΟ to be a bellwether for boundedness is that Ο have an angular derivative of modulus less than 1 at a point on βπ». We raise the question of whether this angular-derivative condition is also necessary for CΟ to be a bellwether for boundedness.