Despite impressive advances in the AdS_{3}/CFT_{2} correspondence, the setup involving Ramond-Ramond backgrounds, which is related to the D1-D5 system of branes, remained relatively poorly understood. We use the mirror thermodynamic Bethe ansatz (TBA) equations recently constructed by Frolov and Sfondrini to study the spectrum of pure Ramond-Ramond AdS_{3}×S^{3}×T^{4} strings. We find that the leading-order contribution to the anomalous dimensions at small tension is due to the gapless world-sheet excitations, i.
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