Process integration is motivated from economic benefits, but it also impacts on the plant behavior introducing interactions and in many cases making the process more difficult to control and operate. During the operation utility flow rates and bypasses are widely used for effective control of process stream target temperatures, but the number of utility units is usually less than the number of process streams in the network and some bypasses should be selected. This paper addresses the optimal bypass design for heat exchanger networks. It consists in a model-based iterative procedure considering controllability metrics and worst-case disturbance rejection with minimum economic penalty. This is essentially a piecewise linearization approach producing excellent results. The methodology proposed is demonstrated using a case study with 3 different structures, making possible a comparison among different options on a quantitative basis, taking into account the optimal operation attainable with minimum total annual cost. These results clearly point out for the need of a simultaneous framework for design with controllability and profitability. The main goal of this work is to contribute within the field of optimal operation and control of HENs and the definition of the operational controllability concept.