Concentration of minor and trace elements in host mineral phases has been estimated using a new approach which avoids difficulties in the direct analysis of complexly intergrown ores using existing techniques, such as neutron activation of grain concentrates of only limited purity, or the relatively high detection limit of the electron microprobe. In contrast, the new method utilizes a general relationship between whole-rock composition, i.e., gold or silver assays, mineral abundance, and mineral composition. Assuming limited compositional variation over relatively short distances in individual drill hole intervals, least squares regression provides a best fit of mineral composition to systems of linear mass balance equations relating whole-rock assays to mineral abundance. Matrix algebraic methods using singular value decomposition have been applied to over 1,000 composite samples in the Butte District of Montana. Maximum estimated precious metal contents in sulfides within the zoning patterns described in parts per million are: chalcocite-digenite, 926 ppm Ag, 5 ppm Au; bornite, 1,075 ppm Ag, 3 ppm Au; chalcopyrite, 211 ppm Ag, 2 ppm Au; pyrite, 9 ppm Ag, 0.3 ppm Au. Locally, and with significantly greater uncertainties, covellite appears to contain up to 10,000 ppm Ag (1 wt %), and enargite-tennantite contains up to 1,700 ppm Ag.--Modified journal abstract.