Radial tire having: a crown surmounted by a tread provided with at least one radially outer elastomer layer intended to come into contact with the road when the tire is rolling; two non-stretchable beads, two sidewalls connecting the beads to the tread, a carcass reinforcement passing into the two sidewalls and anchored in the beads; a crown reinforcement or belt positioned circumferentially between the carcass reinforcement and the tread; a radially inner elastomer layer, (tread “sublayer”), having a formulation different from the formulation of the radially outer elastomer layer, and positioned between the radially outer layer and the belt, wherein the sublayer comprises a rubber composition having at least from 30 to 100 phr of a nitrile/butadiene rubber having a content of butadiene units of between 40% and 90% by weight and more than 30 phr of a reinforcing filler. This sublayer limits the migration of plasticizers in the elastomer layer of the tread towards the inner elastomer compositions of the crown.