Techniques are discussed for measuring radial velocities with precisions of 1-3 kms-1 for late-O, B and early A spectral-type stars of all v sin i from spectra obtained with CCD detectors. Two spectral regions have been investigated, one centered near H-delta at lambda 4073 angstrom and one centered in the Balmer series at lambda 3787 angstrom. At each region the spectra spanned approximately 140 angstrom at almost-equal-to 40 km s-1 resolution. Stellar radial velocities were measured through cross-correlation techniques following the algorithms of Tonry & Davis (1979). We have produced a set of synthetic spectra densely distributed in temperature and projected rotation velocity for use as template spectra in the correlation analyses and for study of systematic errors in the analysis procedure. With careful selection of filters applied to the object and template spectra before cross correlation, we have found that reasonable object/template mismatches in spectral type and rotation velocity typically produce systematic errors of less than 1 km s-1. Sequentially repeated observations show that root-mean-square measurement errors of better than 1 km s-1 can be achieved for narrow-lined stars and better than 2 km s-1 for rapid rotators. In practice, over several years of observing, root-mean-square measurement errors of 1-3 km s-1 are typical. In terms of measurement precision at a given signal-to-noise, the performance of the lambda 3787 angstrom region is superior to that of the lambda 4073 angstrom region for stars with large v sin i. Observations of early type members of the Pleiades and alpha Persei open clusters establish that our radial-velocity zero point for the early type stars is consistent with that for late-type stars to about 1 km s-1. Observations of candidate early type radial-velocity standards are also presented.