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It has recently been showed that lattice/structured codes can outperform random/unstructured codes in a number of scenarios of distributed source coding. One such instance involves lossy distributed compression of linear functions of Gaussian sources, which is the focus of this paper. Existing structured schemes employ “good” lattices for quantization and binning, however, the remaining correlation between the lattice coset indices are not exploited in an efficient way, leading to suboptimal performance when the target distortion is small. This paper proposes a new lattice-based scheme that is capable of eliminating the redundancy among coset indices and achieving a smaller sum-rate than existing schemes. The main novelty lies in the use of a hidden relationship between the coset planes of the quantization indices, and the enlarged set of choices for the quantizers as well as the linear estimation coefficients.