A data processor in which execution threads may be grouped together into thread groups in which the plural threads of a thread group can each execute a set of instructions in lockstep, one instruction at a time. The data processor comprises a plurality of execution lanes for executing respective execution threads of a thread group. For each thread group in a pool 51 of thread groups available to be issued to the execution lanes, an indication 54 of the active threads of the thread group is stored, and sets of at least one thread group from the pool 51 of available thread groups to issue 73 to the execution lanes for execution are selected 72 based on the indications of the active threads for the thread groups in the thread group pool.