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Many applications in a variety of scientific domains produce datasets that consist of a data field lying on a sampling grid that may not be uniformly spaced. However, progressive access for visualization, exploration, and communication of these datasets is a critical issue, and wavelet-based embedded coding an attractive solution given its prior success in realms such as image coding. As grid information may compose a significant portion, or even a majority, of that of the overall dataset, coding the grid as initial overhead is often impractical. Approaches for the joint embedded coding of data and grid are proposed using first-generation wavelet transforms so as not to require prior grid knowledge for transform inversion. In one proposed technique, two independently generated embedded codings, one for data and one for grid, are interleaved. As an alternative, an embedded vector-valued coder, in which data and grid are combined into a single vector-valued field, is considered. Experimental results are reported that favor the former approach over the latter.