The modelling of many voltammetric experiments can be carried out expeditiously by making use of semiintegration or its converse, simedifferentiation. The virtue of this approach is that the modelling, be it algebraic, simulative or numerical, takes place in one dimension only--that of time--rather than in the dual dimensions of space and time. However, the applicability of pure semiintegration is limited to experiments in which transport is by planar semiinfinite diffusion, preceded by a state in which no current flows, and without concurrent homogeneous reactions. In this article it is demonstrated that all these limitations may be overcome by broadening the concept of semiintegration to include other convolutions that reduce to semiintegration in the short-time limit. Appropriate convolutions are derived for spherical and cylindrical geometries, for thin-layer and Nernst-layer electrodes, for faradaic processes complicated by homogeneous reactions of the EC, CE and ECE varieties, and for voltammetry preceded by a steady state, but this list does not exhaust the possibilities. Although controlled-current experiments are most readily modelled by the extended semiintegral approach, a powerful procedure is described by which numerical one-dimensional modelling is applicable to controlled-potential voltammetry. Three worked examples are presented in detail : constant-current chronopotentiometry at a wire electrode; a Nernst diffusion layer problem in which the current is shared by a faradaic path and by double-layer charging; and cyclic voltammetry complicated by a following chemical reaction.