For use in a wide-issue processor, a mechanism for, and method of, conditionally executing instructions and a digital signal processor (DSP) incorporating the mechanism or the method. In one embodiment, the mechanism includes: (1) a conditional execution block state machine that tags and generates link pointers for instructions located in a conditional execution block and (2) conditional link pointer registers, associated with stages in a pipeline of the processor, that contain and cause the link pointers to move therethrough as the instructions located in the conditional execution block move through the stages.