A basic idea of the so-called geometrical approach is to construct "control variations." Heuristically, if one can construct control variations in all possible directions, then the considered control system is small-time locally controllable. The main result of the present paper is a sufficient condition for obtaining high-order control variations. The proof is based on a general Lie series formalism. The relation between the main result and two well-known sufficient controllability conditions is explained. Two illustrative examples are also presented.