  Over the past three decades, synthetic data methods for statistical
disclosure control have continually evolved, but mainly within the domain of
survey data sets. There are certain characteristics of administrative
databases, such as their size, which present challenges from a synthesis
perspective and require special attention. This paper, through the fitting of
saturated count models, presents a synthesis method that is suitable for
administrative databases that is tuned by two parameters. The method allows
large categorical data sets to be synthesized quickly and allows risk and
utility metrics to be satisfied a priori, that is, prior to synthetic data
generation. The paper explores how the flexibility afforded by two-parameter
count models (the negative binomial and Poisson-inverse Gaussian) can be
utilised to protect respondents' - especially uniques' - privacy in synthetic
data. Finally, an empirical example is carried out through the synthesis of a
database which can be viewed as a good substitute to the English School Census.
