We perform a systematic study of the 56 Ni mass (M Ni) of 27 stripped-envelope supernovae (SESNe) by modeling their light-curve tails, highlighting that use of" Arnett's rule" overestimates M Ni for SESNe by a factor of∼ 2. Recently, Khatami & Kasen presented a new model relating the peak time (t p) and luminosity (L p) of a radioactively powered supernova to its M Ni that addresses several limitations of Arnett-like models, but depends on a dimensionless parameter, β. Using observed t p, L p, and tail-measured M Ni values for 27 SESNe, we observationally calibrate β for the first time. Despite scatter, we demonstrate that the model of Khatami & Kasen with empirically calibrated β values provides significantly improved measurements of M Ni when only photospheric data are available. However, these observationally constrained β values are systematically lower than those inferred from numerical simulations, primarily because the observed sample has significantly higher (0.2–0.4 dex) L p for a given M Ni. While effects due to composition, mixing, and asymmetry can increase L p none can explain the systematically low β values. However, the discrepancy can be alleviated if∼ 7%–50% of L p for the observed sample comes from sources other than radioactive decay. Either shock cooling or magnetar spin-down could provide the requisite luminosity. Finally, we find that even with our improved measurements, the M Ni values of SESNe are still a factor of∼ 3 larger than those of hydrogen-rich Type II SNe, indicating that these supernovae are inherently different in terms of the initial mass distributions of their progenitors or their explosion mechanisms.