In the last two decades, with the availability of new state-of-the-art production logging devices that are capable of providing accurate downhole rate and pressure measurements, variable-rate testing has been given special concern. This is mainly because it is sometimes impractical and often impossible to hold a constant flow rate long enough to perform a drawdown test. Furthermore, the use of sandface flow rate and pressure data in well test analysis has a few major advantages over conventional methods. Variable-rate tests minimize the wellbore storage effects, reduce the test duration, and provide better description of the area in the vicinity of the wellbore. This paper presents a new technique that does not require a constant flow rate for the entire duration of the test. The technique consists of two flowing periods: a short constant flow rate period followed by a variable flow rate period. In deriving the final working equation, the variable flow rate period is approximated by a polynomial. The new method can be also used to analyze pressure drawdown data dominated by wellbore storage and pressure buildup data pertaining to early time afterflow. Two simulated cases and two field examples are presented to illustrate the applicability of the new technique.