Site velocities are a common product of continuous Global Positioning System (CGPS) networks. Estimation of site velocities from their time series can be biased if offsets are present. If left uncorrected, offsets can dominate velocity uncertainties. Artificial (nontectonic) discontinuities may arise from environmental and equipment changes or human intervention and error. Analysis of present GPS data sets reveals that on a component by component basis, one offset occurs every 9 years, although it could be as frequent as one offset every 2 years. The effect offset estimation has on rate uncertainty depends on the noise characteristics in the series. If the noise is white, then estimating a single offset in the center of the series doubles the uncertainty. If the noise is random walk, then neither the position nor the number of offsets in the time series seriously alters the rate uncertainty. Undetected offsets in the time series mimic random walk noise. If an offset detection algorithm is implemented, then there is threshold size below which the algorithm can select the wrong offset epoch. Offset position uncertainty increases as offset size decreases. However, small offset position uncertainties will still result in lower rate uncertainties with respect to undetected offsets. Despite the appeal of estimating offsets by detrending and averaging data either side of the discontinuity, such a strategy only serves to increase the rate and offset uncertainties. The best strategy is still to use the maximum likelihood estimator to simultaneously estimate the linear parameters and the noise components.