It's Belfast in the 1980s and Colm (BARRY McEVOY), a Catholic, has just started work as a barber at the local mental hospital. Along with his Protestant coworker, George (BRIAN F. O'BRYNE), Colm gives the various patients haircuts, but realizes there must be more in life for him than doing that. He gets the chance to pursue something more when he hears about a patient known as the Scalper (BILLY CONNOLLY), who once had a monopoly on the entire hairpiece business in Northern Ireland until he scalped several of his customers.
Sensing a lucrative business opportunity, Colm and George convince the Scalper to give up his client list and they then set out to learn everything about selling hairpieces, much to the amusement of Colm's mother (RUTH McCABE) and girlfriend, Bronagh (ANNA FRIEL). They're eventually successful, however, in making their first sale with their new company, The Piece People, but then realize that they have competition from another business, Toupee or Not Toupee.
From that point on, they race against their competitors to sell the most hairpieces before Christmas Eve, with the winner being assured of having the monopoly of the business. Yet, they must contend with customers who won't pay, an I.R.A. man (COLUM CONVEY) who wants the two to supply the I.R.A. with hairpieces, and an overzealous investigator who wants to nail that man.