Universities north of the border are calling on the Scottish Funding Council (SFC) to relax its rules on over-recruitment following an early "spike" in acceptances after the publication of the Scottish Higher results.
A number of institutions fear that they may incur financial penalties from the SFC as prospective students rush to accept places offered to them after the release of the results last week. Many are choosing not to take a gap year or look for work because of the tough employment market.
Liz Lister, director of student recruitment, admissions and marketing at the University of Edinburgh, said: "We have to model on previous years what we think will be the likely uptake of the offers we make.
"This year, a number of extraordinary factors have impacted on that. The uptake of our offers was higher than expected."
Ms Lister said Edinburgh also expected to face a hike in the number of students taking up their insurance offers, as English institutions will be more strict about entry requirements due to the cap on student numbers.
Once universities offer places, they are legally obliged to accept those students if they achieve the required grades.
Robin McAlpine, public affairs manager at Universities Scotland, said the SFC should understand the position that universities find themselves in this year.
"It has got to realise the very pressured circumstances that have led to an increase in acceptances this year," he said.
"We trust that people will understand that universities have acted in good faith - they should not be penalised."
David Bleiman, assistant general secretary of the University and College Union Scotland, also called on the funding council to relax its policy on penalties for over-recruitment.
However, the SFC said that the regulations would not be relaxed, although it added that open recruitment was allowed in certain subjects, such as science, technology, engineering and mathematics. The extra places are not funded but do not incur penalties.
Other subjects, including the creative arts, are allowed a 10 per cent increase in numbers without institutions being penalised.
Heriot-Watt University is seizing the opportunity to expand.
The university, which specialises in open-recruitment subjects such as engineering, expects to increase its student body by 15 per cent this year.
Mike Bates, director of recruitment and admissions at the institution, said: "The university strategy is to grow its numbers, and we are using the current environment to do so."
Pass rates for Scottish Highers and Advanced Highers improved marginally this year, up 2 per cent compared with 2008 for Advanced Higher candidates.