A processing system 2 includes a processing pipeline 12, 14, 16, 18, 28 which includes fetch circuitry 12 for fetching instructions to be executed from a memory 6, 8. Buffer control circuitry 34 is responsive to a programmable trigger, such as explicit hint instructions delimiting an instruction burst, or predetermined configuration data specifying parameters of a burst together with a synchronising instruction, to trigger the buffer control circuitry to stall a stallable portion of the processing pipeline (e.g. issue circuitry 16), to accumulate within one or more buffers 30, 32 fetched instructions starting from a predetermined starting instruction, and, when those instructions have been accumulated, to restart the stallable portion of the pipeline.