We consider the problem of channel intrinsic randomness, which consists in extracting uniform random numbers from the output of a channel independently of its input. We refine existing results by providing new exponents for the exponential decay of the variational distance between the extracted process and the uniform distribution. In particular, our exponent exhibit an improved behavior at rates close to capacity. We also apply this result to the problem of secret key generation, which combines Slepian-Wolf coding and channel intrinsic randomness.