In this paper we study experimentally the properties of three types of quantum -optical random-number generators and characterize them using the available National Institute for Standards and Technology statistical tests, as well as four alternate tests. The generators are characterized by a trade-off between, on one hand, the rate of generation of random bits and, on the other hand, the degree of randomness of the series which they deliver. We describe various techniques aimed at maximizing this rate without diminishing the quality (degree of randomness) of the series generated by it.