Successive interference cancellation, in conjunction with orthogonal convolutional codes, has been shown to approach the Shannon capacity for an additive white Gaussian noise channel. However, this requires highly accurate estimates for the amplitude and phase of each user's signal. We derive an optimal power control strategy specifically designed to maximize the overall capacity under the constraint of a high degree of estimation error. This power control strategy presents a general formula of which other power control algorithms are special cases. Even with estimation error as high as 50%, capacity can be approximately doubled relative to not using interference cancellation. In addition, when properly applied to multicell mobile networks, this power control scheme can reduce the handset transmit power, and therefore other-cell interference, by more than an order of magnitude.