We provide a general mechanism for obtaining uniform information from pointwise data even when the pertinent quantities are highly discontinuous. If a diffeomorphism of a compact Riemannian manifold has nonzero Lyapunov exponents everywhere then the nonwandering set is uniformly hyperbolic. If, in addition, there are expanding and contracting invariant cone families, which need not be continuous, then the diffeomorphism is an Anosov diffeomorphism, i.e. the entire manifold is uniformly hyperbolic. Moreover, the existence of an eventually shrinking cone family (without any transversal information) implies the existence of a continuous and uniformly shrinking cone family what implies partial uniform hyperbolic directions. This is joint work with Y. Pesin and B. Hasselblatt.