Table 1 Four Systems That Have Small Ratios, P/P_surface, but Still Have Significant Eccentricities APOGEE_ID log g P (days) sigma_P (days) e sigma_e P/P_surface 2M05272385+1246432 3.55 1.0529 0.0001 0.15 0.02 1.7 2M11482364+3504215 3.47 3.69 0.01 0.32 0.09 3.6 2M15042105+2700026 2.41 36.68 0.04 0.61 0.04 2.5 2M16503620-0054432 3.52 3.9823 0.0003 0.38 0.05 3.8 Note. Stellar parameters are for the primary (observed) member of the systems. In all cases, the reported uncertainties on the surface gravities are small, sigma_log g < 0.1.