In this paper, we present a new deconvolution method that removes the dependency of the deconvolved constant-rate drawdown responses on the initial reservoir pressure. It is well known that the late-time periods in particular of the deconvolved responses from the recent pressure-rate deconvolution methods are dependent on the initial reservoir pressure. A small error in the initial reservoir pressure could make a significant difference in the late-time periods of the deconvolved responses that can lead to an incorrect interpretation model, particularly misinterpretation of the boundaries. The new method presented is based on pressure-derivative data rather than pressure data that are used in all published deconvolution algorithms. Using pressure-derivative data in deconvolved leads to a nonlinear least-squares objective function that is different from those used in the earlier deconvolution methods and eliminates the dependency of the deconvolved responses on the initial reservoir pressure. Therefore, the new method minimizes incorrect interpretation because of an error or uncertainty in the initial reservoir pressure. We apply the new method to both simulated and field pressure-transient data sets. The results show that the new method oilers a significant advantage over the earlier deconvolved methods for pressure-transient-test interpretation in cases where the initial reservoir pressure is unknown or uncertain.