A method will be presented for extracting rules from a labelled speech database in order to find context-dependent allophone rules. The classical approach to this problem involves parameter fitting by e.g. least-squares error minimization on a sufficiently large dataset. In that approach, the type of interaction is often to be chosen beforehand. Moreover, there remains a general problem, how to improve the output of linearly ordered rule sets. The present algorithm searches for the interaction in a broad class which can be modified interactively It is partly based upon the classical approach, and partly on (non-linear) matrix manipulation. From the theory, we will discuss the question, how to construct an 'optimal' linearly ordered rule set.