The disclosure provides methods and apparatus relating to random access in a wireless communications network. In one aspect, a method in a user equipment comprises: detecting an event triggering a random access procedure; determining an adjustment for a random access parameter as a function of one or more of: a type of the event triggering the random access procedure; and a characteristic of data to be transmitted or received by the UE upon completion of the random access procedure; applying the adjustment to a configured value for the random access parameter to obtain an adjusted value for the random access parameter; and performing the random access procedure with a base station operable in the wireless communications network, using the adjusted value for the random access parameter.