Summary: The authors study the relation between the excess of open manifolds and their topology by using the methods of comparison geometry. They prove that a complete open Riemannian manifold with Ricci curvature negatively bounded from below is of finite topological type provided that the conjugate radius is bounded from below by a positive constant and its excess is bounded by some function of its conjugate radius, which improves some results in S. L. Xu et al. [Math. Appl. 15, No. 4, 7–12 (2002; Zbl 1029.53044)].