Instructions are fetched and issued by an instruction fetch and issue circuit with the instructions' sizes in program order. An allocate circuit allocates reservation station entries in a reservation station circuit, and reorder buffer entries in a reorder circuit, for the issued instructions in order, storing the instructions' sizes in the allocated reorder buffer entries. The reservation and dispatch circuit dispatches the issued instructions to the execution circuits for execution when they are ready. The execution circuits store the result data including target addresses of branch instructions into the corresponding reorder buffer entries. During each retirement operation, a retire circuit reads the instruction sizes and the target addresses for a predetermined number of issued instructions from their allocated reorder buffer entries. The retire circuit determines two or more speculative next instruction pointers for each of the issued instructions, factoring into consideration whether the issued instructions are branch instructions or not, and their relative positions to each other. Each of the speculative next instruction pointers indicates what the next instruction pointer for the processor should be for retiring a particular combination of the result data values of the issued instructions under consideration. The retire circuit conditionally updates the next instruction pointer with one of the speculative next instruction pointers, depending on how many, if any, of the instructions can actually retire, and whether any of the actually retiring instructions are branch instructions.