Microaggregation is a statistical disclosure control technique for microdata disseminated in statistical databases. Raw microdata (i.e., individual records or data vectors) are grouped into small aggregates prior to publication. Each aggregate should contain at least k data vectors to prevent disclosure of individual information, where k is a constant value preset by the data protector. No exact polynomial algorithms are known to date to microaggregate optimally, i.e., with minimal variability loss. Methods in the literature rank data and partition them into groups of fixed-size; in the multivariate case, ranking is performed by projecting data vectors onto a single axis. In this paper, candidate optimal solutions to the multivariate and univariate microaggregation problems are characterized. In the univariate case, two heuristics based on hierarchical clustering and genetic algorithms are introduced which are data-oriented in that they try to preserve natural data aggregates. In the multivariate case, fixed-size and hierarchical clustering microaggregation algorithms are presented which do not require data to be projected onto a single dimension; such methods clearly reduce variability loss as compared to conventional multivariate microaggregation on projected data.