Bitplane coding is a common strategy used in current image coding systems to perform lossy, or lossy-to-lossless, compression. There exist several studies and applications employing bitplane coding that require estimators to approximate the distortion produced when data are successively coded and transmitted. Such estimators usually assume that coefficients are uniformly distributed in the quantization interval. Even though this assumption simplifies estimation, it does not exactly correspond with the nature of the signal. This work introduces new estimators to approximate the distortion produced by the successive coding of transform coefficients in bitplane image coders, which have been determined through a precise approximation of the coefficients' distribution within the quantization intervals. Experimental results obtained in three applications suggest that the proposed estimators are able to approximate distortion with very high accuracy, providing a significant improvement over state-of-the-art results.