Private schools have followed national trends by seeing a dip in A-level success.
The pass rate for top grades achieved by A-level entrants from fee-paying schools remains almost double the UK average.
But the number of A-level entries from private school pupils awarded at least an A grade dropped to 48.7%, down from 49.3% the previous year. The national average for 2016 is 25.8%.
And the proportion of pupils achieving at least one A* was 17.9%, down 0.6 percentage points on the previous year - though still ahead of the national average of 8.1%, itself down by 0.1 percentage point.
The figures, compiled by the Independent Schools Council (ISC), are based on data from 495 independent schools across the UK.
They suggest that one in 15 candidates (6.8%) got at least three A* grades, down slightly from one in 14 (7%) the previous year.
The overall pass rate was 99.1% - one percentage point better than the national average.
The proportion of students getting an ABB grade remained at 55.5%.
Barnaby Lenon, ISC chairman, said: "A concerted effort to halt grade inflation in recent years has seen the top grades both nationally and in independent schools level off and fall slightly, so it is encouraging to see the headline A* and A figure remain solid.
"Of particular note is the number of students achieving ABB grades, which will see many of them moving on to the university of his or her choice, a high number to the top institutions.
"Importantly, the actual grades achieved remain impressively high. ISC schools focus strongly on the 'facilitating' subjects which are much prized by top universities. In 2015 our schools had record levels of entry to Russell Group universities and we expect this trend to continue."
Julie Robinson, ISC general secretary, said: "The annual exam results each August remind us all that the academic side of school life is a top priority and that the grades achieved help pave a foundation for much that is to come for many young people.
"On top of all other aspects of independent school life, visible recently with the sporting successes of our alumni in the Olympics, these results show there is great strength and continued value in independent education."
The figures also show that the number of students taking the International Baccalaureate rose by 5% compared with last year. Candidates taking the Extended Project Qualification went up by 12%, while Btec entrants rose by 14%.
The ISC's survey takes into account the results of 36,992 candidates.