It is this quality above all, he believes, that has encouraged Notre Dame high in Sheffield to thrive and make the chief inspector's list of the nation's most successful schools.
"Where we have succeeded most is in creating an ethos that is characterised by a caring attitude that includes demanding the best of pupils," he said.
"I think a lot of schools manage to be either caring or driven by high standards, but not both."
Notre Dame high is a Roman Catholic mixed comprehensive with specialist technology college status.
Its 1,200 pupils arrive with attainment levels in line with the national average, but leave (at either 16 or 18) significantly ahead of their peers.
Since 1992, when Mr Conwy took over as head, the number of youngsters achieving five or more A*-C GCSEs has soared from 39 to 63 per cent.
A key factor in the school's success is its strong team of administrators, employed to take as much of the paperwork out of teachers' hands as possible.
The school also has a highly-developed system of self-evaluation that constantly monitors progress.
Teachers observe each other in action so that good practice can be shared. Detailed statistics are also kept on the performance of every pupil and member of teaching and non-teaching staff to identifiy where action needs to be taken to improve.
Mr Conway said: "I would put a lot of our success down to the fact that we are a Catholic school and are concerned with turning out young people who have developed, not just academic-ally, but emotionally, spiritually and socially. That said, I can assure you our pupils are not always little angels."