The University of Edinburgh has introduced a new Access Threshold programme ahead of the new academic year, which lowers the grades required by prospective students hoping to gain a place.
Applicants for its law degree will be required to have one A and three B grades at Scottish Higher level for entry - below the five A grades typically required.
Similarly for applications to medicine, pupils will be required to gain three A grades and two B grades - below the expected four As and one B.
A spokesman for the University of Edinburgh said applications would be considered based on a “range of factors” and not just on grades earned.
He said: “The university is committed to widening access and welcomes applications from students from diverse backgrounds, while ensuring we support every student throughout their academic journey.
“Our contextualised admissions process allows us to make offers to Widening Participation applicants, who meet the minimum academic requirements, using our Access Threshold - which takes into account a range of factors other than academic qualifications.
“The 2019-20 Access Threshold for each degree is published on our online degree finder.
“We continue to explore opportunities to further adjust our requirements.”
Figures published earlier this year by the Higher Education Statistics Agency indicated more than 15% of students entering university in Scotland last year were from the country’s most deprived areas.
The Scottish Government has set a target that 16% of students entering university will be from the most deprived backgrounds by 2021, with that figure increasing to 20% by 2030.
The University of Glasgow and the University of Aberdeen have also published two sets of entry requirements for each course.
A spokesman for the University of Glasgow said: “The University of Glasgow is committed to widening access to higher education and we have a proud history of outreach programmes, of which contextualised offer-making to applicants from varied backgrounds is an important part.
“Those contextualised offers have been made since the 1980s via our Summer School programme.
“Our widening access programmes currently cover the 120 secondary schools in the west of Scotland and areas of disadvantage across the country.
“Combining effective outreach with evidence-based contextualised admissions is the key to our success.
“While we’re delighted with the progress we’ve made, we are constantly working to bring equity of opportunity to all widening access participants.”
Alastair Sim, Universities Scotland director, said universities are making the move because it is “the right thing to do”.