40Ar/39Ar experiments on melt-inclusion-bearing quartz (MIBQ) from the Bishop and Bandelier Tuff Plinian deposits indicate high concentrations of excess 40Ar in melt inclusions. Two rhyolite glass melt inclusion populations are present in quartz; exposed melt inclusions and trapped melt inclusions. Air-abrasion mill grinding and hydrofluoric acid treatments progressively remove exposed melt inclusions while leaving trapped melt inclusions unaffected. Laser step-heating of MIBQ yields increasing apparent ages as a function of exposed melt inclusion removal, reflecting the higher nonatmospheric 40Ar concentrations hosted in trapped melt inclusions. Exposed melt inclusion-free MIBQ from the Bishop, Upper Bandelier, and Lower Bandelier Tufts yield total-gas ages of 3.70 ?? 1.00 Ma, 11.54 ?? 0.87 Ma, and 14.60 ?? 1.50 Ma, respectively. We interpret these old apparent ages as compelling evidence for the presence of excess 40Ar in MIBQ. Trapped melt inclusions in sanidine phenocrysts may contain excess 40Ar concentrations similar to those in MIBQ. This excess 40Ar has the potential to increase single-crystal laser-fusion ages of sanidine by tens of thousands of years, relative to the actual eruption age.