They boasted international talents Jay-Jay Okocha, Ivan Campo and Youri Djorkaeff, mixed with the hardened Englishmen like Kevin Davies and Kevin Nolan.
They regularly punched above their weight and finished inside the top eight between the 2003/04 and 2006/07 seasons.
One man who could have joined them in 2004 was Brazil World Cup winner Rivaldo.
The former European footballer of the year was 32 at the time and looking for a new club.
"We have taken in all kinds of waifs and strays, people who were out of shape and out of sorts and we've turned them into proper players again," Allardyce told Sky Sports.
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"Sometimes it just comes down to putting an arm around a player and making him feel wanted again. Football can be a lonely environment when you are on a downer.
"Even the best players can feel lost when things turn against them which I think is what has happened in Rivaldo's case."
Even the players were talking up his arrival and telling him what to expect.
Davies said: "You've got to work hard in this team. We've got some good players in but they have not worked hard and been left out. So we will see how good he is at tracking back! If Rivaldo does sign, we are going to learn loads from him, like we do from other players here."
He was a free agent at the time having had his contract terminated by AC Milan in November 2003.
Rivaldo had won the Champions League with the club, but had been relegated to the bench by manager Carlo Ancelotti.
A move to Bolton beckoned, but things swiftly changed and the then-Premier League club pulled out of the deal.
"I can categorically confirm that Rivaldo will not be joining us," Allardyce told the club's official website.
He had looked set for a move to Qatar before making a quick U-turn and signed for Olympiacos in Greece.
Bizarrely, Rivaldo then played a friendly against Bolton in 2008 when he was at AEK Athens and talked about the move.
"Four years ago I met the manager and the chairman but in the end we could not reach an agreement, which meant I didn't sign for Bolton," he said. "I cannot say why it didn't happen. It is a great shame.
"The Premier League is a very strong league and I would like to have played in England for Bolton.
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"When I am not playing here in Greece I watch a few games. The Premier League is a good competition and it's great to watch."
Rivaldo sadly was never another chapter in the legendary Sam Allardyce Bolton team of the 2000s.