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We demonstrate theoretically that a simple two-coupled-ring structure yields very narrow resonances in the transmission spectra, provided the loss is very small. The linewidth is smallest when the path lengths of the two rings have a ratio of two. Relative to the single ring, the linewidth is reduced beyond the size scaling by the intensity buildup factor in the second ring. In the lossless case, the linewidth can be two orders of magnitude narrower. The enhancement can still be seen for experimentally demonstrated silicon-on-insulator microrings.