A method, network node and wireless device that use grants that restrict the set of LCHs that can be serviced using the grant are disclosed. According to one aspect, a method in a wireless device (WD) configured to communicate with a network node is provided. The method includes receiving from the network node, a first grant for uplink transmission of data, the first grant indicating that use of the first grant is restricted to logical channels (LCHs) of a first subset of LCHs of an LCH set, the first subset of LCHs configured to include fewer than all LCHs, such that there exists at least one LCH for which use of the first grant is not allowed. The method also includes selecting at least one LCH from the first subset of LCHs according to a priority of LCHs in the first subset of LCHs, the selected at least one LCH configured to provide data to be transmitted on the uplink according to the first grant.