Each instruction thread in a SMT processor is associated with a software assigned base input processing priority. Unless some predefined event or circumstance occurs with an instruction being processed or to be processed, the base input processing priorities of the respective threads are used to determine the interleave frequency between the threads according to some instruction interleave rule. However, upon the occurrence of some predefined event or circumstance in the processor related to a particular instruction thread, the base input processing priority of one or more instruction threads is adjusted to produce one more adjusted priority values. The instruction interleave rule is then enforced according to the adjusted priority value or values together with any base input processing priority values that have not been subject to adjustment.