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An edge-emitting LED coupled to a single-mode fiber shows increased coupling sensitivity to fiber displacement compared with multimode fiber. Sensitivity to lateral misalignment in the direction perpendicular to the junction plane of the LED increases by at least a factor of three, regardless of the coupling scheme used. A reciprocal relationship between peak coupling efficiency and sensitivity to misalignment is observed. We show that a previous theory for laser coupling can be extended to include edge-emitting LED's, and that it predicts this relationship. The results for different coupling schemes are discussed with respect to LED packaging.