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We report on transport measurements in fields up to 16 T in clean, untwinned single crystals of YBa2Cu3O7 which indicate that there is a critical end point for first-order melting in the H-T phase diagram in the mixed state of that system. Our data show that at a well defined value of the magnetic field, the phase boundary sharply changes slope where the first-order melting transition gives way to a second-order vortex-glass transition. These data suggest that the recently observed first-order transition is robust in the presence of a finite amount of disorder and that the vortex-glass transition only occurs for disorder beyond a certain critical amount. (Author)