Process plants are often divided into logically identifiable regions, each having associated processing tasks. Such regions are necessary when considering the practical features of plant design such as operational flexibility, safety, plant-layout, etc. The regions are therefore more generally described as "areas of integrity". This paper introduces the subject of heat recovery between areas of integrity. While this is new to the heat integration literature the problem is well known in practice. It is straightforward nowdays to predict the minimum overall energy consumption for such heat-integrated systems. However, this can be achieved by several different schemes for heat flows between the areas. The task then becomes identifying those schemes which offer maximum area integrity when seeking minimum energy, with say the least number of interconnections between the regions. This paper develops some understanding of the problem and gives a procedure for finding the required heat flows between areas. The results are made available as targets, before any network design. Thereafter, a method is shown which translates the heat flow schemes into actual network designs.