In this paper an approach is developed for compressing a multiway array prior to estimating a multilinear model with the purpose of speeding up the estimation. A method is developed which seems very well-suited for a rich variety of models with optional constraints on the factors. It is based on three key aspects: (1) a fast implementation of a Tucker3 algorithm, which serves as the compression method, (2) the optimality theorem of the CANDELINC model, which ensures that the compressed array preserves the original variation maximally, and (3) a set of guidelines for how to incorporate optional constraints. The compression approach is tested on two large data sets and shown to speed up the estimation of the model up to 40 times. The developed algorithms can be downloaded from http:\\newton.mli.kvl.dk\foodtech.html.