Technical Abstract: Synthetic weather generation models often rely on standard uniform random numbers (RN) to simulate stochastic aspects of weather. However, short sequences of RNs, needed to generate certain weather variables, are not necessarily uniformly distributed, as assumed by weather generation models, and may lead to unrepresentative synthetic weather. A modified random number generator (MRNG) was developed that ensures that sequences as short as 50 RNs meet the uniformity requirement of the weather generation model. The procedure consists of compositing a population of 30 numbers that meet the uniform distribution requirements, and sampling, one at a time, at random and without replacement, from this population. As more RNs are needed a different population of 30 numbers is composited, and so forth. Tests of the MRNG revealed that sequences of about 50 RNs from the MRNG consistently approximated both mean and standard deviation of the uniform distribution within ±5%. Sequence lengths of 50 RNs and longer were shown to be serially uncorrelated and distribution invariant. Generation of daily precipitation with RNs produced by the MRNG led to better approximations of observed daily precipitation statistics than with RNs from a conventional RNG. A frequency analysis of generated annual peak daily precipitation showed good correspondence with observed precipitation for all peak-precipitation events with return period less than 2 years, and a slight overestimation for higher frequency peak events. It was concluded that the MRNG is a better choice for source of RNs because the RNs are more compatible with assumptions of the weather generation model and lead to higher-quality synthetic daily precipitation records, especially short records of 50 years.