McLeish saw his side finish ninth in the top flight last year on the back of a record which saw them collect 17 points on their travels.
This season began with another creditable result away from St Andrew's - a 2-2 draw on the road at Sunderland - and McLeish expects another thorough examination of that form when his side travel to Bolton on Sunday afternoon.
He said: "Bolton have a record to preserve but so do we as we are both unbeaten so far this season.
"We had a good record away from home last season and we would like to try and do as well as we did last season on that front.
"But that will be a big task.
"We took teams by surprise last year but we are not a surprise package anymore.
"There is a little bit more pressure on us but I believe the players have the mentality and the toughness to stand up to everything."
McLeish is hopeful of adding Wigan winger Charles N'Zogbia to his squad before Tuesday's transfer deadline but is confident one player who has already joined the club can play his part this season.
Former Blackburn striker Matt Derbyshire arrived on loan from Olympiacos last week and scored his first goal for the club in last night's 3-2 Carling Cup win over Rochdale.
Derbyshire will be back in the north west on Sunday and is no stranger to the Reebok, having featured in two wins there for Rovers in recent years.
He is likely to be on the bench as McLeish partners giant Nikola Zigic with Cameron Jerome again but the boss believes he will weigh in with his fair share of goals for the club this term.
He said: "He got brighter as the game went on against Rochdale.
"We didn't see much of him in the first half thanks to Rochdale's performance but you got a glimpse of what he can do when from the first good pass of the night he won us a penalty.
"He has good movement and is always looking to get in behind or down the sides.
"He started to look very dangerous in the second half in and around the box. He got his goal and linked up well with others.
"We think he can score goals and hope he will be a good acquisition for us."
James McFadden is a doubt to face the Trotters after being replaced at half-time against Rochdale with a groin problem.
But the likes of Ben Foster, Barry Ferguson and Craig Gardner should all return after being rested.