The highest TAS (and therefore groundspeed in still air) staying below the barber's pole (max IAS) for a given Mach number can be got at FL280/FL290. I regularly used to gain 15 minutes flying a 737-200 on a four hour flight flying at M0.74 at FL280 compared with M0.72 at FL350. Not the most economical way to fly but helped with schedule keeping and flight time limitations. In the early days of BKK-LHR and SIN- LHR I believe BA 747s flew home at FL280 at M0.86(?) this saved up to an hour on higher levels (although could be bumpy across the Bay of Bengal in the monsoon!) and meant less Cabin crew required, lower premium payments etc.