In a recent article (Goncalves et al., AIChE J. 2017. DOI: 10.1002/aic.15556), we presented a mixed-integer linear programming formulation for the detailed design of shell and tube heat exchangers based on the Kern approach (Kern, D. Q Process Heat Transfer; McGraw Hill, 1950). The formulation relies on the use of standardized values for several mechanical parts, which we express in terms of discrete choices. Because we aim at having this model used as part of more complex models (i.e., heat exchanger networks synthesis), we identified a need to improve its computational efficiency. In this article, we explore several different modeling options to speed up solutions. These options are based on different alternatives of aggregation of the discrete values in relation to the set of binary variables. Numerical results show that these procedures allow large computational effort reductions.