The cylindrical end of the shaft of a rotating valve door in an automotive HVAC case is closely supported without either excessive clearance or binding, accommodating expected tolerance variations in the final, assembled location of the shaft end. The expected tolerance range is divided up into components along, and perpendicular to, the direction in which two housings of the case are assembled. One slot is cut into one housing along the direction of assembly, and another perpendicular thereto. When the housings are assembled, the two slots cross one another, capturing the shaft end closely on all four sides between the two pairs of slots. The closed ends of the slots have enough clearance from the nominal location of the shaft end to let the shaft end float to its final location without binding.