Embodiments provide a method of controlling a flow of pipeline fluid through a pipeline pig that includes a bypass channel and at least one relief channel extending therethrough. The method includes (a) inserting the pipeline pig into a pipeline through which the pipeline fluid is flowing, (b) increasing a differential pressure established in the pipeline fluid between a trailing end and a leading end of the pipeline pig such that the differential pressure sequentially reaches a pre-selected minimum relief pressure, a pre-selected maximum relief pressure and a pre-selected minimum bypass pressure, (c) opening the at least one relief valve to permit the pipeline fluid to flow through the relief channel when the differential pressure reaches the pre-selected minimum relief pressure (d) closing the at least one relief valve to restrict the flow of pipeline fluid through the relief channel when the differential pressure reaches a pre-selected maximum relief pressure, and (e) opening a bypass valve to permit the pipeline fluid to flow through the bypass channel when the differential pressure reaches the pre-selected minimum bypass pressure.