This paper is concerned with the reduction of conservatism on stabilization conditions of discrete-time Takagi-Sugeno fuzzy models via delayed nonquadratic Lyapunov functions. A fruitful approach recently appeared in the literature, which, despite its benefits, dramatically increases the number of linear matrix inequalities needed to synthesize a controller. The two sets of sufficient conditions hereby proposed tackle this numerical problem while reducing conservatism and increasing the stabilization domain of existing conditions in literature, as illustrated in several examples.