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Dirty-paper codes have been used extensively as the basis for new code design for digital image watermarking due to their interference rejection property. Random bending attacks still pose a great danger to watermark survival and the theoretical basis for the assessment of their impact on decoder performance is yet to be laid. Meanwhile, past research results point out to the use of a new channel model named additive white Gaussian noise and jitter (AWGN&J) channel as a means to assess the impact of imperfect synchronization in the performance of the watermark decoder. In this paper, we show that the capacity of the ideal Costa scheme is greatly reduced in the presence of imperfect synchronization and that its host signal interference rejection property does not hold anymore in the presence of such attack. Moreover, we show that arbitrarily increasing watermark power does not help to mitigate the effect of imperfect synchronization.