The problem considered is the choice of a set of system parameters, so that inequality constraints are satisfied or can be satisfied by tuning, for a specified variation of parameter values about their nominal value. Such problems occur when systems must be synthesised from components whose values are known only to certain tolerances. Fully implementable algorithms that are suitable for the general nonconvex cases and utilise concepts employed by Eaves and Zangwill in their generalised cutting plane algorithms are presented. The algorithms generalise earlier algorithms for the pure tolerance (no tuning) and the tolerance-tuning problems that are suitable only for the case when the tolerance and tuning regions are constant.