Be flexible by a few days
Premium fares are priced by demand, and demand varies a lot by day. Moving your departure by two or three days, or flying midweek, can change the price noticeably. Search a few date combinations before you decide.
Avoid peak weeks
Summer holidays, Christmas and New Year, and big events fill premium cabins with leisure travellers. Spring and autumn often bring lower fares on long-haul routes.
Search the whole city, not one airport
Use city codes like NYC, LON or TYO rather than a single airport. They cover all the main airports in that city, so you see every option.
Try a nearby departure city
Fares from a larger hub are sometimes much lower than from a smaller city nearby. If the saving is big enough, a short positioning flight or drive can be worth it.
Compare one-way and round trip
On some routes, two one-way tickets cost less than a round trip, or let you mix airlines. Try both trip types.
Check what the seat is
Business class seats vary widely. On long flights, look for a fully flat bed with direct aisle access. On short flights within the US, "first class" is usually a wider recliner, not a bed.
Consider premium economy
On daytime flights or trips under about seven hours, premium economy can give much of the comfort for a fraction of the price.