Bolton were drawn in the same Uefa Cup group as German giants Bayern Munich, but Everton and Tottenham will fancy their chances of making progress.
Spurs face a reunion with Anderlecht, the team they beat in the 1984 final, while Everton's main threat is likely to come from Dutch side AZ Alkmaar.
Aberdeen must overcome Greek outfit Panathinaikos and Atletico Madrid.
But it is Bolton, with Portuguese side Braga and Red Star Belgrade joining Bayern, who face the stiffest test.
Each team will play two matches at home and two away with the group stage starting on 25 October and the top three going through.
They will be joined by eight third-placed teams from the Champions League groups for the knockout round.
25 Oct - SC Braga (h)
8 Nov - Bayern Munich (a)
29 Nov - Aris Thessaloniki (h)
6 Dec - Red Star Belgrade (a)
Bolton, Everton and Tottenham will play alternate games home and away and all start their campaigns hosting SC Braga, Larissa and Getafe respectively.
Bolton's second game on 8 November sees them face the tough trip to Bayern Munich and they have to travel to play Red Star Belgrade in a potentially crucial final group game on 6 December.
25 Oct - Larissa (h)
8 Nov - FC Nuremberg (a)
5 Dec - Z St. Petersburg (h)
20 Dec - AZ Alkmaar (a)
Bolton striker Nicolas Anelka says his side need to try to win their home games and attempt to earn a point on their travels.
He has cited his French international team-mate Franck Ribery as one of Bayern's main threats.
Anelka told the club's website: "I would love to go there (Munich) and upset the world of football by winning. It would put Bolton on the map in terms of being a European force.
"The match against Red Star will be evry intimadating. they always seem to raise their game in European competition and their fanatical fans are always very passionate at home."
25 Oct - Getafe (h)
8 Nov - Hapoel Tel Aviv (a)
29 Nov - Aalborg (h)
6 Dec - Anderlecht (a)
Everton's final game is a trip to AZ Alkmaar on 20 December, while Spurs end with a visit to Anderlecht on 6 December.
"I am pretty satisfied," said Spurs boss Martin Jol at his side's draw.
"You can only assess it on paper on at the moment and my feeling is that it could have been a lot tougher for us.
"Anderlecht away will be a hard one, but it is in the final game for us and, hopefully, we will have done the business by then.
25 Oct - Panthinaikos (a)
8 Nov - Lok Moscow (h)
5 Dec - Atletico Madrid (a)
20 Dec - FC Copenhagen (h)
"They have got fanatical supporters, just like we've got, so that should be a special night with the history between the two clubs in this competition."
UEFA CUP DRAW
Zenit St Petersburg
Red Star Belgrade