Hearts were given a much tougher task than Rangers in the draw for the first-ever group stage in the Uefa Cup.
Rangers, among the top seeds, were drawn in Group F with Auxerre (France), Grazer (Austria), Amica Wronki (Poland) and AZ Alkmaar (Netherlands).
Hearts, who were fourth seeds, must face Feyenoord (Netherlands), Shalke 04 (Germany), Basle (Switzerland) and Ferencváros (Hungary) in Group A.
Feyenoord, Shalke and Basel all have good recent European pedigrees.
Two Rangers players will be relishing the opportunity to face their former clubs following Tuesday's draw.
Dutch international Fernando Ricksen joined Rangers under former manager Dick Advocaat in a £3.6m deal from Alkmaar in the summer of 2000.
French defender Jean-Alain Boumsong arrived at the Glasgow club from Auxerre in the summer.
Rangers have met Auxerre previously, in 1996-97, when the French club won 2-1 both home and away in the group stages of the Champions League.
Auxerre are currently fourth in the French league, three points behind leaders Lille.
Grazer also lie fourth in their domestic league, five points behind leaders Austria Vienna, having won the domestic title for the first time last season.
They defeated Liverpool 1-0 at Anfield in this season's qualifying for the Champions League but went out on aggregate after losing 2-0 at home.
Amica Wronki are third in the Polish league, five points behind leaders Wisla Krakow.
Alkmaar are fifth in the Dutch league, seven points adrift of PSV Eindhoven.
Of the teams in Rangers' group, only Auxerre have made much progress in European competition in recent seasons.
But Hearts have been pooled with Dutch giants Feyenoord, who are now coached by former Chelsea and Newcastle boss Ruud Gullit.
Feyenoord, who lost 8-7 on penalties to Rangers in a pre-season friendly after a 0-0 draw, are second top in the Dutch league, three points behind PSV and won the Uefa Cup in 2002.
Shalke, Uefa Cup winners in 1997, are seventh in the German Bundesliga, nine points behind Wolfsburg, but interest from German television could provide a financial windfall for Hearts.
Basle, presently top of the Swiss league, defeated Celtic in the Champions League qualifying stages in 2002.
Ferencváros have a two-point lead in the Hungarian top division and defeated Millwall to qualify for the group stage.
Rangers' ties:
Amica Wronki (away) 21 October
Grazer (home) 25 November
Alkmaar (away) 2 December
Auxerre (home) 15 December.
Hearts' ties:
Feyenoord (away) 21 October
Shalke (home) 4 November
Basle (away) 25 November
Ferencváros (home) 16 December.