A simple, rapid, and robust algorithm for the design of segmentally baffled shell and tube heat exchangers is presented. The algorithm ensures full use of the maximum allowable pressure drops given typically as design specifications, with no geometric restrictions on the equipment. The core of the algorithm is provided by two compact formulations that relate the pressure drop for each side of the exchanger with the film heat transfer coefficient and the exchanger area. The compact formula for the tube side includes the effects of tube ends while the one for the shell side is based on the Bell-Delaware method. The parameters of the compact formulas are used as search variables in the design algorithm. Two examples are presented that show how the algorithm compares to other reported design methods and how the search for realistic solutions is aided by this method.