The city is considering different models following a report by Bill Coyle, the number-crunching consultant and timetabling guru in the former Strathclyde Region, and may sanction a number of pilots if parents and other agencies support the principles.
One model would increase the number of teaching periods to 33 a week from the 30 which has been the norm for many years. Maximum class contact time would be cut by an hour to 22.5 hours in line with the McCrone agreement, while the pupil week would stay at 27.5 hours. That leaves a difference of 300 minutes for headteachers to grapple with.
A 33-period week could lead to a seven-period day with schools starting as early as 8.45am and taking only 40 minutes for lunch. Some staff, however, are concerned about the shortened break and the possibility of having three consecutive 50-minute periods - two and a half hours of non-stop teaching.
The format would do away with registration time first thing in the morning, a move many teachers are said to oppose. A second option is a 32-period week with 10 minutes a day for registration and pastoral duties. Computerised registration, however, could eliminate that and make the 33-period week more attractive.
The city has been holding a series of seminars with senior managers and staff. One headteacher said that he favoured a 33-period week because of the flexibility in organising Standard grade and Higher Still courses.
Jim Dalziel, head of Eastbank Academy, who is discussing proposals with staff, is excited by the opportunity to re-examine the basics. "The ideas have the potential to deliver a whole range of things in raising attainment and in relation to McCrone. The important thing is to devise a model that works for each individual school."
Ken Cunningham, head of Hillhead High and president of the Headteachers' Association of Scotland, said: "We always welcome opportunities to structure the school day to meet the needs of the learning environment. The curriculum is becoming more flexible with more vocational courses and anything that we can do to deliver that more effectively we would look at. But it's very much something that relates to an individual school."
Heads are now tweaking various models to suit their own school and maximise class contact time. Some want to cut the number of Standard grades from eight to seven and finish school earlier on certain days to allow for department meetings.
Larry Flanagan, chair of the Educational Institute of Scotland's local branch, said the union was "neither for nor against" the proposals, although it would be looking at the implications.