Head teachers of leading independent schools have accused exam regulators of creating a "smokescreen" around soaring numbers of appeals over exam marking.
Last week, the head of exam watchdog Ofqual suggested some schools were making "strategic" use of challenges to A-level and GCSE grades.
But the chairman of the Headmasters' and Headmistresses' Conference said the "real issue is inaccurate marking".
Ofqual has said it is planning improvements to the appeal process.
The university sector's Supporting Professionalism in Admissions organisation has also called for "greater clarity" about the rising numbers of appeals and grades being changed.
Director Janet Graham said: "This is an area that the awarding organisations and Ofqual could explore in more depth."
Ofqual chief Glenys Stacey faced questions last week from the Education Select Committee about the process of challenging exam results.
Ms Stacey told MPs she wanted a system that was "swift, effective and fair".
In the past four years, the number querying results has more than doubled to more than 400,000 and the number getting their grades changed after re-marking has also more than doubled to more than 77,000.
But Chris King, Headmasters' and Headmistresses' Conference (HMC) chairman and headmaster of Leicester Grammar School, said there needed to be much more transparency and information about the grades being challenged and changed.
He also criticised the suggestion the increase in appeals was being driven by schools gaming the system to improve their grades
"It is misleading to imply that schools who appeal wrong grades are actually a cause of the problem. This is a smokescreen," said Mr King.
Instead he blamed "inconsistent marking and grading and a Byzantine appeals process, which Ofqual itself acknowledges is inadequate".
"Any suggestion that schools of any kind are 'gaming' the appeals system is unfair and underserved," said Mr King.
Exam boards charge for re-marking, unless there is a grade changed, with schools and parents paying millions of pounds each year.
"Independent schools submit proportionally more appeals but naturally state schools put in far more than we do, and we welcome this. Ultimately this is about justice for hard working pupils, whatever school they go to," said Mr King.
Ofqual has said that only about 1% of the overall exam results are subsequently changed and that proposals to improve the process of appealing against GCSE and A-level results would be announced later this month.