Now down in Spain's third tier after slipping into financial administration, Alaves's typical opponents these days include the B teams of several top-flight sides rather than the giants of European football.
Their run to the UEFA Cup final won them many admirers as they dispatched Inter Milan and Kaiserslautern before falling to Liverpool after an own goal from full back Delfi Geli four minutes from the end of extra time.
While fans gathered at the Vitoria-based club's Mendizorroza stadium for Tuesday's last-32, first leg against Barca will be looking forward to seeing Lionel Messi and Andres Iniesta in the flesh, coach Natxo Gonzalez has issued a warning to his players.
"Against an opponent like that you cannot enjoy yourself," Gonzalez said after his side's 1-0 league win at Logrones at the weekend.
"If you go out and try to enjoy playing Barca they'll put 10 goals past you.
"We have to go out on the pitch prepared to win. I am convinced we can do it and my mission is to transmit that conviction to the players so they believe it while also knowing that it's going to be very tough," added Gonzalez.
The last time Alaves faced Barcelona in the Copa del Rey, a 5-2 aggregate defeat in the last 16 in January 2007 when Javier Saviola scored all five goals for the opposition, they had just been relegated to the second division.
The format of the earlier rounds makes it extremely difficult for lower-ranked sides to progress as the first leg is played at their stadiums, giving the big guns home advantage for the return match.
Many believe this robs the competition of much of the romance of the David against Goliath upsets that have added to the allure of equivalent competitions in England, Germany, Italy and France.
Some shocks do still occur. Mirandes reached the semi-finals last season and fellow third-tier side Alcorcon, now in the second division, knocked out Real Madrid 4-1 on aggregate three years ago.
A number of minnows have a chance to deal a blow to more illustrious rivals this week with Alcoyano hosting Real Madrid on Wednesday and Jaen at home to Atletico Madrid the same day.
Llagostera play Valencia on Tuesday and Eibar are at home to 2012 runners-up Athletic Bilbao on Thursday.
There are four all-La Liga clashes with Real Zaragoza hosting Granada, Real Valladolid at home to Real Betis, Sevilla welcoming Espanyol and Deportivo Coruna entertaining Real Mallorca.
Local hero and Real Madrid fan Juan Carlos Ferrero, a former tennis world number one who retired last week, will perform the honorary kickoff at Valencia-based Alcoyano's match against Jose Mourinho's side, Copa del Rey winners in 2011.
- Sports & Recreation