We've found 2 phrases for expedite (0.162 seconds):

grease payment »    A bribe or extorted money, usually relatively small in amount, provided to a low-level government official or business person, in order to expedite a business decision, shipment, or other transaction, especially in a country where such payments are not unusual.

lubrication payment »    A bribe or extorted money, usually relatively small in amount, provided to a low-level government official or business person, in order to expedite a business decision, shipment, or other transaction, especially in a country where such payments are not unusual.

BTW, Why won't you become an editor?