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Phase recovery in vestigial sideband (VSB) data transmission is discussed. Examining a particular aspect of this broad area, attention is focused on the time required to recover carrier phase in order to achieve a satisfactory error rate. We derive the acquisition time for simple models. Our results are exhibited graphically, relating pertinent system parameters. These results indicate that while in double sideband transmission the acquisition time required to achieve a satisfactory error rate is of the order of a few symbol intervals, in VSB transmission this time grows to tens and hundreds of symbol intervals.