Radial velocities for the early-type stars in the Pleiades cluster have always been challenging to measure because of the significant rotational broadening of the spectral lines. The large scatter in published velocities has led to claims that many are spectroscopic binaries, and in several cases, preliminary orbital solutions have been proposed. To investigate these claims, we obtained and report here velocity measurements for 33 rapidly rotating B, A, and early F stars in the Pleiades region, improving significantly on the precision of the historical velocities for most objects. With one or two exceptions, we do not confirm any of the previous claims of variability, and we also rule out all four of the previously published orbital solutions, for HD 22637, HD 23302, HD 23338, and HD 23410. We do find HD 22637 to be a binary but with a different period (71.8 days). HD 23338 is likely a binary as well, with a preliminary 8.7 yr period also different from the one published. Additionally, we report a 3635 day orbit for HD 24899, another new spectroscopic binary in the cluster. From the 32 bona fide members in our sample, we determine a mean radial velocity for the Pleiades of $5.79\pm 0.24\,\mathrm{km}\,{{\rm{s}}}^{-1}$ , or $5.52\pm 0.31\,\mathrm{km}\,{{\rm{s}}}^{-1}$ when objects with known visual companions are excluded. Adding these astrometric binaries to the new spectroscopic ones, we find a lower limit to the binary fraction among the B and A stars of 37%. In addition to the velocities, we measure $v\sin i$ for all stars, ranging between 69 and 317 $\mathrm{km}\,{{\rm{s}}}^{-1}$ .
