Generally, mathematical programming for heat exchanger network (HEN) design uses variables resulting from a decomposition of the temperature range in intervals, based on potential pinch points. In this paper an approach using only lumped variables is presented. It reintroduces the information that is involved in the decomposition in intervals, by means of additional constraints. As a result, smaller and more flexible models involving the minimum number of required continuous variables, are available. This is advantageous especially when many iterative calculations should be carried out, e.g. in combinatorial search procedures. To demonstrate this approach, two cases have been worked out.