Stir together salt, allspice, and cayenne. Pat pork dry and sprinkle spice rub all over pork, pressing to adhere.
Heat oil in a 12-inch heavy skillet over moderately high heat until hot but not smoking, then brown pork, 1 tenderloin at a time, on all sides, about 1 minute each. Transfer as browned to a large roasting pan and arrange 2 inches apart.
Roast in middle of oven until an instant-read thermometer inserted diagonally 2 inches into center of each tenderloin registers 155°F, 20 to 25 minutes. Let pork stand 5 minutes before slicing.
