This paper reports the findings of a systematic study using Monte Carlo experiments and a real dataset aimed at comparing the performance of various ways of specifying random taste heterogeneity in a discrete choice model. Specifically, the analysis compares the performance of two recent advanced approaches against a background of four commonly used continuous distribution functions. The first of these two approaches improves on the flexibility of a base distribution by adding in a series approximation using Legendre polynomials. The second approach uses a discrete mixture of multiple continuous distributions. Both approaches allow the researcher to increase the number of parameters as desired. The paper provides a range of evidence on the ability of the various approaches to recover various distributions from data. The two advanced approaches are comparable in terms of the likelihoods achieved, but each has its own advantages and disadvantages.