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Extension of the molecular rate equations for a dye laser to include the effect of very rapid transverse flow shows that spatial transit times comparable to the dye intersystem crossing time prevent the buildup of a large triplet state population. This new technique enables limiting the triplet-triplet absorption loss without using triplet quenching agents. An air-turbine driven rotating disk of rhodamine 6G dye in polymethyl methacrylate is used to exchange the dye times per second by 250-m/s transverse flow through the pump beam waist in an end-pumped near-spherical cavity ( ). In pulse experiments, transverse flow enabled increase of power output by a factor of 2.5 with a corresponding decrease in threshold power of about 30 percent. Thermal defocusing effects are eliminated at much slower flow rates. The ultrafast transverse-flow technique should also be applicable to liquid dye lasers and would be most important for cases where no effective triplet quenching agent can be found.