Copyright notification and enforcement, authentication, covert communication, and hybrid transmission are examples of emerging multimedia applications for digital watermarking methods, methods for embedding one signal (e.g., the digital watermark) within another 'host' signal to form a third, 'composite' signal. The embedding is designed to achieve efficient trade-offs among the three conflicting goals of maximizing information-embedding rate, minimizing distortion between the host signal and composite signal, and maximizing the robustness of the embedding. Quantization index modulation (QIM) methods are a class of watermarking methods that achieve provably good rate-distortion-robustness performance. Indeed, QIM methods exist that achieve performance within a few dB of capacity in the case of a (possibly colored) Gaussian host signal and an additive (possibly colored) Gaussian noise channel. Also, QIM methods can achieve capacity with a type of postprocessing called distortion compensation. This capacity is independent of host signal statistics, and thus, contrary to popular belief, the information-embedding capacity when the host signal is not available at the decoder is the same as the case when the host signal is available at the decoder. A low-complexity realization of QIM called dither modulation has previously been proven to be better than both linear methods of spread spectrum and nonlinear methods of low-bit(s) modulation against square-error distortion-constrained intentional attacks. We introduce a new form of dither modulation called spread-transform dither modulation that retains these favorable performance characteristics while achieving better performance against other attacks such as JPEG compression.