Capello's England team, still under a cloud after their dismal World Cup display, visit Hitzfeld's goal-shy Switzerland for what is expected to be the most difficult match in their Euro 2012 qualifying campaign.
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Germany's Hitzfeld, winner of an extraordinary seven Bundesliga and two Champions League titles, is under growing pressure over Switzerland's failure to find the net.
Italian Capello, winner of four Serie A, two La Liga and one Champions League title, may take a long time to win back confidence after England's lame display at the World Cup, although their 4-0 win over Bulgaria in their opening Group G match on Friday was a good start.
Both men showed signs of fraying nerves after their team's matches on Friday.
Hitzfeld lost patience when the St Gallen crowd jeered striker and record Swiss scorer Alexander Frei after he missed a penalty in the goalless friendly draw at home to Australia.
"The way that a few fans treated him was embarrassing," said Hitzfeld, suggesting that Switzerland should avoid playing at St Gallen in the future. "Alexander Frei has given great service to the team."
Switzerland were widely criticised for their defensive style at the World Cup, where they went out in the first round despite a 1-0 win over eventual winners Spain in their opening game.
It turned out to be their only goal at the tournament, a problem throughout Hitzfeld's two years at the helm.
Capello snapped after being asked if he deserved more respect. "Respect is not the right word because 'respect' in Italy means something different. The word 'respect' has a lighter meaning in English," he retorted.
Capello will look to ensure that his side hit the ground running, repeating the sharp passing and incisive running that tore through Bulgaria in the opening 20 minutes and which was such a filip after the fear-fuelled stodge of the World Cup.
His concern is that as the second goal failed to materialise the players lost their way somewhat and allowed their opponents to grab a toehold.
Joe Hart, installed as first choice goalkeeper having been an unused number three in South Africa, was forced to make several good saves, not least on the hour at 1-0 when Bulgaria were really pressing.
The defence looked disorganised at times and, with regular centre back partners Rio Ferdinand and John Terry being joined by Michael Dawson on the injured list, Capello must throw together another untried pairing against the Swiss.
Phil Jagielka, whose pace and movement belie his insistence that he still does not feel worthy of an England shirt, is certain to be one of them with either Gary Cahill, who made his debut off the bench as Dawson's replacement on Friday, Matthew Upson or Joleon Lescott alongside him.
Probable line-ups:
Switzerland: Diego Ben
