In the days Pre-RVSM, I took a K (Mk 1 IIRC) up to FL370. Empty, not alot of gas, and it was 'kin cold all the way up. It was also a particularly airtight 'frame, so I just kept going up until we hit max diff at a cabin alt of 8,000ft. It was late night / early morning, so no traffic to get in the way of.
Shame the J is limited to FL280 by not having enough / correctly reporting altimeters. It goes up like a rocket and then hits an administrative glass ceiling!