Eccentricity versus orbital period. We plot the sample of MSP + WD binaries mainly from the ATNF catalogue (Manchester et al. 2005, with a few others, compiled by Hui et al. 2018), differentiating between those with minimum WD mass above and below |$0.45\ {\rm M}_{\odot}$| (orange triangles and blue circles, respectively). We show our objects with magenta stars. The grey line is the theoretical relation for MSP + He WD binaries formed through stable MT derived by Phinney (1992). The points circled in red are eMSPs (e.g. see Stovall et al. 2019, for a description of the five plotted here). We also circle in green two binaries with massive CO WDs with large eccentricities (Lorimer et al. 2015; Berezina et al. 2017).