For reducing the restart pressure of streams selected from waxy crude oils, water-in-crude emulsions and dispersions of hydrocarbon hydrates, at least partially structured, a mechanic disturbance is applied, in flow-stop conditions, on the streams. The temperatures are lower than the WAT (Wax Appearance Temperature) for the waxy crude oils and water-in-crude emulsions. The temperatures are also lower than the forming temperatures of the hydrates and pressures higher than the forming pressure of the hydrates, for the dispersions of hydrocarbon hydrates.