The City of Edinburgh Music School has 36 pupils, based between Flora Stevenson primary and Broughton Secondary, but the council cautions against extending the range of interests beyond sport and some aspects of the arts.
"It could be argued that the number of subjects which require specialist facilities, staff, early identification of talent - over and above what is available to pupils within mainstream education - are few," the city states in its response to a Scottish Office consultation paper.
It argues that instrumental music teaching needs sustained one-to-one contact and access to group music-making. But it is broadly opposed to centres of excellence and believes pupils should have their needs met in their local school. "Integration of the gifted is seen as having significant advantages for schools as well as for pupils."
Instead of a specialist school in information technology, a network of teachers could use flexible learning materials and electronic links.
Another option may be to organise national initiatives based on local provision.
In sport, Edinburgh backs more opportunities for talented pupils at school, neighbourhood and city levels, followed by national and international levels, rather than a designated school.