The present disclosure relates to the prioritization of devices taking part in a multi-user random access wireless communication. Based on some known conditions, devices that comply with the conditions are given preferential treatment during the random access period. The preferential treatment may refer to the eligible devices being allowed to access more resource units during the random access, or it may also mean faster access to the medium during the random access. By taking advantage of the methods described in the present disclosure, it is possible to assign higher priority to selected frame types and/or device categories in a multi-user random access wireless communication system.