Kenny Dalglish admits he faces an unpleasant selection call for Sunday's Carling Cup final against Cardiff City with Liverpool at full strength for the club's first appearance at Wembley since 1996.

Craig Bellamy and Daniel Agger have both recovered from the back problems that ruled them out of the FA Cup win over Brighton & Hove Albion last weekend and, with the exception of the long-term absentee Lucas Leiva, Dalglish will have a full squad to choose from against the Championship side. The duo's availability leaves the Liverpool manager with arguably the toughest selection decision of his 13 months back in charge at Anfield.

Bellamy has been outstanding in Liverpool's progress to their first domestic final in six years and had an injection in his back last week in order to be fit to play against his boyhood and former club. He is likely to be direct competition for a place with Stewart Downing who, despite a subdued start to his Liverpool career following a £20m move from Aston Villa last summer, impressed in the 6-1 win over Brighton last Sunday.

The availability of Agger would impact on the Anfield stalwart Jamie Carragher's prospects of starting at Wembley for the first time with Liverpool.

Dalglish, who is looking to complete a clean sweep of English domestic trophies as a manager, said: "It is always difficult to leave players out and that is a great credit to the players because they have all done well. Every one of them has competed and has wanted to compete for their positions in the team. It is not pleasant to leave anyone out and Sunday will be no different.

"The principle for us is the same as it has always been and that is to put out a team that is going to win a game. It doesn't mean you are undermining anyone in any way, shape or form. We will never be successful if we think we've only got 11 players."

Like Downing, Andy Carroll also impressed against Brighton and has shown a marked improvement in form over recent weeks to enhance his chances of starting against Cardiff. City's veteran striker, Kenny Miller, has identified the £35m Carroll – who was omitted from Stuart Pearce's England squad for next week's friendly with Holland – as a major threat to his side's prospects of causing what would be a considerable upset.

Miller said: "It's bad for us that he seems to be coming into a good spell before this game because he is a top striker. You don't become a bad player overnight. What you saw in the six months in the Premier League with Newcastle is a top, top player and a young lad as well.

"What he has done, he's not hid, he's still going out there every week, putting himself in the firing line to get chances. There was no doubt he was going to come good. He might have turned a corner."

Cardiff have lost their past two games at Wembley – the 2008 FA Cup final against Portsmouth and the 2010 Championship play-off final against Blackpool – and Miller admits it would be a career highlight if Malky Mackay's underdogs defeat the seven-times League Cup winners Liverpool.

The former Rangers and Celtic striker said: "It would probably be one of the biggest achievements [of his career]. When you play in Scotland for an Old Firm team you're expected to win cups. This is a different scenario altogether.

"We're underdogs and rightly so because we are playing a top team. But if we can impose our game on them and get our big players on the ball, I think we can pose problems."