Embodiments herein relate to a wireless device (10) for handling access to a radio base station (12) in a wireless communication network (1), the wireless device (10) being configured to: initiate a random access procedure in the wireless communication network (1); determine that a problem with the random access procedure has occurred when a certain condition is fulfilled; and perform at least one of the following, when determined that a problem with the random access procedure has occurred: delay a next random access preamble transmission attempt; abort from a higher layer the random access procedure immediately; and stop the random access procedure at a lower layer.