More "rigorous and demanding" A-levels would make student admissions fairer, Cambridge University says.
Most Cambridge students get three grade As or better at A-level
The university, most of whose students gain three grade As or better, claims the current system makes it hard to differentiate between highly able applicants.
In its draft response to a government taskforce report on university admissions, Cambridge backs the idea of expanding Advanced Extension Awards - set at a higher level - to help achieve this.
It also demands more assessment of skills such as critical thinking, problem-solving, essay-writing and extended argument.
An interim report by the government's university access taskforce, published in April, said all applicants should be able to show their "potential", as well as academic achievement.
But ways of measuring this must not amount to "social engineering", it added. The report also said there were problems defining the term "merit".
The taskforce, chaired by Brunel University vice-chancellor Steven Schwartz, concluded that "equal examination grades [at A-level] do not necessarily represent equal potential", where leading universities were concerned.
It said some extra qualities, such as enthusiasm and motivation, were important to selection.
Cambridge's response says candidates must be "considered as individuals, judged on their own merits, without partiality and bias".
It sometimes accepted students with "lower attainment levels" than three A grades at A-level, to allow for "educational disadvantage or disruption".
But qualities other than academic achievement were hard to quantify, so there was a danger that publishing data on these could bring more "unrealistic applications".
The pressure of numbers of candidates for places at leading universities is high, the Cambridge response adds.
It says: "This does not mean that the admissions process itself is unfair.
"It does mean that applicants must not be led to believe they have a 'right' to a place at any given university."