Blum, Micali (1982), Yao (1982), Goldreich, Goldwasser and Micali (1984), and Luby, Rackoff (1986) have constructed random number generators, random function generators and random permutation generators that are perfect if certain complexity assumptions hold. We propose random number generators that pass all statistical tests that depend on a small fraction of the bitstring. This does not rely on any unproven hypothesis. We propose improved random function generators with short function names and which minimize the number of pseudo-random bits that are necessary for the evaluation of pseudo-random functions. We announce a new very efficient perfect random number generator.