Sheffield University still has places free on over 200 of its degree courses - but only for students with the very best A-level grades.
Rules have changed this year giving universities no recruitment limit on students who scored at least an A and two Bs on their courses.
It means top universities are effectively in competition to attract the best candidates to courses that in previous years would by now have been full.
Sheffield is still recruiting for a wide variety of degrees through the clearing system, including archaeology, zoology, biology, history, engineering and maths.
A spokesman confirmed it still had places for good candidates.
He added: “The university has currently met its target number of places. However due to the Government’s decision to allow universities to recruit as many high achieving students as they are able, we are still recruiting some additional high quality students in some subject areas through clearing and adjustment.”
Previously each university was allocated a set number of students and places were full soon after the A-level results were published.
Now some institutions are offering a range of incentives to tempt talented sixth-formers, including huge scholarships, cut-price university accommodation and cheap books and computer software.
Numbers of students with the best grades are limited - it is estimated only 115,000 fall into that category.
Other leading universities still on the hunt for more students include Leeds, Liverpool and Newcastle.
Overall student recruitment is up by six per cent so far this year on 2012, to over 450,000 - the second highest figure ever.