is a quantum triangular antiferromagnet, ferromagnetically stacked, with an incommensurate (IC) structure due to a Dzyaloshinskii-Moriya interaction. Because of the classical degeneracy caused by the frustration, fluctuations in have extraordinarily large effects, such as the phase transition in longitudinal magnetic field (normal to the planes, parallel to the IC wavenumber q) and the plateau in q in transverse field (perpendicular to q). We argue that fluctuations are responsible also for the new IC phase discovered in transverse field near the Néel temperature , by Werner et al (Werner T, Weber H B, Wosnitza J, Kelnberger A, Meschke M, Schotte U, Stüßer N, Ding Y and Winkelmann M 1997 Solid State Commun. 102 609). We develop and analyse the corresponding minimal Landau theory; the ground-state reconstruction due to fluctuations is described phenomenologically, by means of a biquadratic term. The Landau theory gives two IC phases, one familiar from previous studies; the properties of the new IC phase, which occupies a pocket of the temperature-field phase diagram near , agree qualitatively with those of the new phase found experimentally.