A systematic experimental study is performed to examine the f-2f technique for sweeping the carrier-envelope phase (CEP) of few-cycle laser pulses by changing the amount of positive dispersion in the extracavity beam path. Slightly changing the dispersion not only changes the CEP but affects the entire spectral-phase function. As a result, large discrepancies are found between the true CEP as independently measured with a stereo-above-threshold-ionization spectrometer and the CEP detected by an f-2f interferometer when sweeping the phase with glass wedges. A new CEP-stabilization scheme is proposed and experimentally shown to significantly improve the performance of CEP sweeping. © 2011 Optical Society of America.