The authors present results for the specific heat of an untwinned YBa₂Cu₃O_7-x single crystal. The specific heat was measured with a resolution better than 50 mK between 85 K and 110 K. The divergence in the specific heat at T_c is extremely sharp with no indication of rounding. It is not possible to fit the divergence by simply adding Gaussian fluctuations to a BCS-like step, however, they find that the divergence does fit a logarithmic divergence very well over nearly three decades between 10^-4< mod t mod <0.1. This can be interpreted either as providing evidence for local pair superconductivity or for a wide crossover region from Gaussian to critical fluctuations.