A least-squares procedure which simultaneously estimates station corrections, event magnitudes, and an attenuation rate is used as a basis for analyzing the variance of explosion magnitudes. This procedure is here termed “joint magnitude determination” (JMD). The JMD method is applied to Seismic Data Laboratory (SDL) data from North American stations for Nevada Test Site explosions. The standard deviation of station magnitudes (MS and mb) computed by JMD for an event typically is one-half of the standard deviation of magnitudes computed by routine methods. This reduction is wholly due to the addition of station terms. Surprisingly, no consequent reduction in scatter of the explosion MS versus mb plot was attained by using JMD estimates rather than routine ones. To resolve this paradox, the scatter of magnitude estimates is divided into three distinct parts: source, path-station, and measurement. The absolute value for each part is derived from the seismic measurements without using yield information. After path-station effects and measurement noise are suppressed, it is found that source effects contribute significantly to magnitude bias for explosions, thus explaining the failure of the JMD method to reduce MS versus mb scatter.