PSR J1802 – 2124 is a 12.6 ms pulsar in a 16.8 hr binary orbit with a relatively massive white dwarf (WD) companion. These properties make it a member of the intermediate-mass class of binary pulsar (IMBP) systems. We have been timing this pulsar since its discovery in 2002. Concentrated observations at the Green Bank Telescope, augmented with data from the Parkes and Nançay observatories, have allowed us to determine the general relativistic Shapiro delay. This has yielded pulsar and WD mass measurements of 1.24 ± 0.11 M ☉ and 0.78 ± 0.04 M ☉ (68% confidence), respectively. The low mass of the pulsar, the high mass of the WD companion, the short orbital period, and the pulsar spin period may be explained by the system having gone through a common-envelope phase in its evolution. We argue that selection effects may contribute to the relatively small number of known IMBPs.