Quins begin their EDF Energy Cup campaign against Llanelli Scarlets at Stradey Park on Sunday, having lost all four league games since returning to top-flight English rugby.
But Quins and England legend Leonard, the world's most capped prop, insists the 16-team cup competition offers an important change of direction.
"Quins just want to record a win this season and get off the mark," said Leonard, whose former club claimed just two losing bonus points from successive defeats against London Irish, Gloucester, Wasps and Leicester.
"There are certain restrictions playing in the Premiership. You want to create that buffer between you and the other teams at the bottom, but the EDF Energy Cup provides players with an opportunity to throw the shackles off."
Quins are in the same pool as Llanelli, Newcastle and Sale Sharks, with only the winners gaining a Millennium Stadium semi-final place next March.
England's 12 Premiership challengers have an added incentive of Heineken Cup qualification through lifting the EDF trophy, and Quins boss Dean Richards parades nine players who were on starting duty for last weekend's league appointment with Leicester.
Magners League leaders Llanelli are without Wales scrum-half Dwayne Peel, who rests an elbow injury, but international team-mates Stephen Jones, Matthew Watkins, Dafydd James and Alix Popham all feature.
Bath's acting head coach Steve Meehan, meanwhile, has adopted a philosophical approach to early-season injury problems that have kept key forwards Steve Borthwick, Gareth Delve and Michael Lipman out of his immediate league and cup plans.
"Injuries don't play as important a role as people may feel running into matches," Meehan said. "If somebody is injured, then he is injured, and we just get on with things.
"We don't drop our heads and cry about it or carry on about it - there is no point.
"We've got a squad to work with and, one way or another, squads are rotated, whether they are rotated as a result of what coaches or selectors are trying to achieve or they are rotated because people are injured.
"That is rugby - that is the nature of the sport."