A peristaltic pump comprising a pump housing, a compressible pump tube positioned between rotatable occluding members and a pump tube track in the housing, where there is an opening in the pump tube track between a first occluding member and a second occluding member such that when the second occluding member has exited occlusion of the pump tube at the opening, a third occluding member completes occlusion of the pump tube thus capturing a compensating volume of fluid between the first and third occluding members, and when the second occluding member reenters occlusion at the end of the opening, it displaces the compensating volume towards the outlet of the pump tube, thus maintaining fluid velocity in the outlet stream.