Methods and apparatuses are provided for controlling power consumption in a processor (or computational unit thereof). The method comprises monitoring power consumption in a processor (or computational unit) and determining that the power consumption of the processor (or computational unit) exceeds a threshold. Thereafter, instruction issuance if modified (such as by slowing or ceasing instruction issuance) within the processor (or computational unit) until the power consumption is below the threshold. The apparatus comprises a power consumption monitor for determining when power consumption within the processor exceeds a threshold. Upon that determination, a scheduler begins modify instruction issuance to one or more execution units until the power consumption is below the threshold. The modification of instruction issuance can be to slow instruction issuance or cease instruction issuance for a time period or until the power consumption is below the threshold.