But when delegates assembled last Friday at the Elektron Hotel in Krakow, they engaged in so much hair-splitting over party strategy that the meeting broke up without deciding on a nomination. Those who were in the thick of things say the trouble started when the party's main faction proposed the party leader, Karel Pleszaty, as the best man to give President Lech Walesa a close electoral shave.
This faction advocated using the slogan: 'Receding, we advance.' But a renegade group objected and proposed instead to back the Speaker of Poland's parliament, Jozef Oleksy, known in some salons as 'the bald-headed Robespierre'. In addition, the dissidents wanted a more rugged party slogan - 'You can't refuse a bald man anything.'
A third faction, representing an outgrowth of the party's youth organisation, Young Semicircle, then raised its head. It suggested that the man to pin the party's presidential hopes on was Jozef Lassota, the mayor of Krakow. 'They can't grind you down if you've got a shiny crown,' was this faction's preferred slogan.
Rapidly, the conference descended into disarray, and a parting of the ways now seems inevitable for the three factions of the Party of the Bald. In this respect, the party's fortunes may turn out to resemble those of the ill-starred Polish Beer Lovers' Party.
Having won 16 parliamentary seats in the 1991 elections, the party split into two movements, Big Beer and Little Beer, but both were swept out of the legislature in elections last September.