  We determine the all-loop dressing phases of the AdS3/CFT2 integrable system
related to type IIB string theory on AdS3 x S3 x T4 by solving the recently
found crossing relations and studying their singularity structure. The two
resulting phases present a novel structure with respect to the ones appearing
in AdS5/CFT4 and AdS4/CFT3. In the strongly-coupled regime, their leading order
reduces to the universal Arutyunov-Frolov-Staudacher phase as expected. We also
compute their sub-leading order and compare it with recent one-loop
perturbative results, and comment on their weak-coupling expansion.
