The students have finished ninth, fourth and third in the past three years and are keen to jump two spots and win the final next month.
Taieri leads the Gallaway Trophy competition with 64 points, followed by Southern 57, University A 45, Dunedin 44, Harbour 42, Alhambra-Union 41, Kaikorai 37, Zingari-Richmond 24, Green Island 6, Pirates 6.
University A is in third spot and has already played second-round games against the other teams in the top four. It beat Dunedin 32-5, but had losses to Taieri (32-29) and Southern (30-21).
The students appear to have an easy run to the semifinals with games against Kaikorai, at the University Oval tomorrow, Pirates, Alhambra-Union and Harbour.
In the first round, University A beat Kaikorai 44-10, Pirates 60-7 and Alhambra-Union 38-12. It was beaten 25-21 by Harbour.
Coach John Hyde is not getting too far ahead of himself.
''I don't like to count my chickens before they hatch,'' he said.
''Kaikorai are always a hard team to play and will be tough this week.''
University's toughest game will probably be against Harbour in the last round of the Gallaway Trophy.
Hyde does not expect Alhambra-Union to be easy.
''They are a tough team to play and they have got some key players back,'' he said.
''We have still got a lot of work to do. If any of those teams kick us over, it will be us done. Our goal is to make the semifinals and we must make sure we don't get complacent.''
University A, like other teams, has been affected by injuries but it now looks a bit brighter.
Ace goalkicker Stephen Fenemor, who had a serious knee injury last winter, has recovered from reconstruction surgery and will have his first start of the season against Kaikorai at the University Oval tomorrow.
''He had a run for the Bs and half a game for us against Southern last week. He is back to full fitness,'' Hyde said.
Fenemor first played for the students in 2011 and had a stellar year in 2012, when he scored 235 points.
The goalkicker for the students this year is Fletcher Smith, who has scored 96 points and should reach the ton tomorrow.
''We'll let Fletcher continue with the goalkicking. But having two players in the side who can kick goals is a bonus for us.''
Otago representative Faasiu Fuatai is expected to return for the game against Pirates tomorrow week.
He was injured when playing for Otago in last year's ITM Cup and has had shoulder reconstruction surgery.
''He also had a cleanup in his knee and had surgery on that, as well,'' Hyde said.
Second five-eighth Shae Tucker, who has been out with a broken finger, is expected to return in time for the semifinals.
Kaikorai should not be taken lightly because its team includes flying wing Bryce Morgan, who has scored 10 tries this season, and first five-eighth Cam Rutherford, who has scored 116 points.
