Many items can be purchased in Jamaica duty free, but most countries have limits as to the amounts that can be taken back. Visitors returning to the US may not carry Cuban cigars, however you can smoke them while in Jamaica .

Duty free limits into the UK are:

200 cigarettes; or 100 cigarillos; or 50 cigars; or 250 gms of tobacco. 2 litres of still table wine. 1 litre of spirits or strong liqueurs over 22% volume; or 2 litres of fortified wine, sparkling wine or other liqueurs. 60 cc/ ml of perfume. 250 cc/ml of toilet water. £145 worth of all other goods including gifts and souvenirs.

For example you are allowed two bottles of rum per person (you are allowed three bottles per person if they are 750 ml in size). If from the States, Cuban cigars are still not allowed. You may buy them & smoke them there, however. On some shopping tours they will take you where items are duty free. Just be sure to ask if you are not sure. Customs in Jamaica are pretty much the same as other places. On your departing flight going through customs they may choose to check your luggage. Don't be alarmed. Going through Security, before boarding the aircraft they look inside purses, and carry ons and it is best to also have your pockets emptied before you walk through the detector.