An undesirable side effect of many watermarking and data-hiding schemes is that the host signal into which auxiliary data is embedded is distorted. Finding an optimal balance between the amount of information embedded and the induced distortion is therefore an active field of research. In recent years, with the rediscovery of Costa's seminal paper Writing on Dirty Paper, there has been considerable progress in understanding the fundamental limits of the capacity versus distortion of watermarking and data-hiding schemes. For some applications, however, no distortion resulting from auxiliary data, however small, is allowed. In these cases the use of reversible data-hiding methods provide a way out. A reversible data-hiding scheme is defined as a scheme that allows complete and blind restoration (i.e. without additional signaling) of the original host data. Practical reversible data-hiding schemes have been proposed by Fridrich et al., but little attention has been paid to the theoretical limits. Some first results on the capacity of reversible watermarking schemes have been derived. The reversible schemes considered in most previous papers have a highly fragile nature: in those schemes, changing a single bit in the watermarked data would prohibit recovery of both the original host signal as well as the embedded auxiliary data. It is the purpose of this paper to repair this situation and to provide some first results on the limits of robust reversible data-hiding. Admittedly, the examples provided in this paper are toy examples, but they are indicative of more practical schemes that will be presented in subsequent papers.