priority mail — (in the U.S. Postal Service) mail consisting of merchandise weighing more than 12 ounces sent at first-class rates.
special delivery — (in the U.S. Postal Service) delivery of mail outside the regularly scheduled hours, by a special messenger, upon the payment of an extra fee.
verb airmail
mail — monetary payment or tribute, especially rent or tax.
send — to cause, permit, or enable to go: to send a messenger; They sent their son to college.
dispatch — to send off or away with speed, as a messenger, telegram, body of troops, etc.