An oilfield pressure control apparatus, comprising: an upper seal member configured to seal around a drill string, wherein the upper seal member comprises a stripper rubber configured to seal around the drill string when the pressure on an exterior side of the stripper rubber is greater than the pressure on an interior side of the stripper rubber, the exterior side of the stripper rubber of the upper seal member facing in a first axial direction; a lower seal member configured to seal around the drill string, wherein the lower seal member comprises a stripper rubber configured to seal around the drill string when the pressure on an exterior side of the stripper rubber is greater than the pressure on an interior side of the stripper rubber, the exterior side of the stripper rubber of the lower seal member facing in a second axial direction opposite the first axial direction; a chamber defined by and located between the upper and lower seal members (26a, 26b); and at least one pressure differential accommodation device (60, 70) in fluid communication with the chamber, wherein the at least one pressure differential accommodation device (60, 70) is configured to compensate for a first change in a pressure within the chamber caused by entrance of a tool joint on the drill string into the chamber via one of the upper and lower seal members (26a, 26b), and to compensate for a second change in the pressure within the chamber caused by exit of the tool joint from the chamber via the other of the upper and lower seal members (26a, 26b), wherein the at least one pressure differential accommodation device (60, 70) comprises a relief valve configured to be in fluid communication with a riser, or, in the case of riser-less drilling operations, the sea above the upper seal member. an upper seal member configured to seal around a drill string, wherein the upper seal member comprises a stripper rubber configured to seal around the drill string when the pressure on an exterior side of the stripper rubber is greater than the pressure on an interior side of the stripper rubber, the exterior side of the stripper rubber of the upper seal member facing in a first axial direction; a lower seal member configured to seal around the drill string, wherein the lower seal member comprises a stripper rubber configured to seal around the drill string when the pressure on an exterior side of the stripper rubber is greater than the pressure on an interior side of the stripper rubber, the exterior side of the stripper rubber of the lower seal member facing in a second axial direction opposite the first axial direction; a chamber defined by and located between the upper and lower seal members (26a, 26b); and at least one pressure differential accommodation device (60, 70) in fluid communication with the chamber, wherein the at least one pressure differential accommodation device (60, 70) is configured to compensate for a first change in a pressure within the chamber caused by entrance of a tool joint on the drill string into the chamber via one of the upper and lower seal members (26a, 26b), and to compensate for a second change in the pressure within the chamber caused by exit of the tool joint from the chamber via the other of the upper and lower seal members (26a, 26b), wherein the at least one pressure differential accommodation device (60, 70) comprises a relief valve configured to be in fluid communication with a riser, or, in the case of riser-less drilling operations, the sea above the upper seal member.