A rigid wheel (18) or roller for a compactor machine, comprising a drum for contacting material to be compacted. The drum has a profiled outer surface including a first cylindrical portion (27) and a second cylindrical portion (29). The first cylindrical portion has a larger rolling diameter than the second cylindrical portion. An inclined portion (24) extends between the first and second cylindrical portions. The area of contact between the outer surface of the drum and refuse, soil or other material to be compacted varies with the depth of penetration of the wheel into the material. The different rolling diameters within the scope of one wheel give different ground pressures. This means that the pressure applied to the material for compaction varies depending upon the depth of penetration of the wheel. One benefit of this wheel/roller design is to allow improved go anywhere mobility--high floatation where needed changing to heavy ground pressure where conditions demand.