A computer processor includes a dispatch stage and a dependency skipping execution unit. The dispatch stage is configured to dispatch a plurality of instructions that include a general purpose instruction configured to produce first data, a dependent instruction configured to produce second data, and an indirect dependent instruction configured to produce third data. The dependency skipping execution unit is configured to monitor the plurality of instructions and to process the indirect dependent instruction in response to the general purpose instruction producing the first data. The indirect dependent instruction is issued independently from the second data produced by the indirect dependent instruction.