The council's eight secondaries have been given two years to cut the number of subjects in the first two years to a maximum of 12. Schools currently offer between 13 and 17 subjects, and some classes see as many as 19 different teachers a week.
Angus is believed to be the first authority to issue advice on ending the curriculum fragmentation following HMI's report last December, Achieving Success in S1 and S2.
Jim Anderson, director of education, who chairs the Scottish Office's 5-14 committee, said: "The HMI report struck a chord with teachers. There is fragmentation which ought to be addressed and we are attempting to be pragmatic in our solutions."
The top priority is to phase cuts over the next two years in the number of "discrete" subjects to 12, reducing the number of teachers in front of first and second-year pupils. Mr Anderson admitted there was "a little bit of anxiety around" and some teachers feared their subjects would be axed.
Government inspectors want only 10 courses but even more radical surgery would be needed to achieve that target, Angus insists.
To reach 12 subjects, the council recommends an end to taster courses of one period a week or less, timetabling integrated science throughout S1 and S2, and teaching only one modern language and a maximum of two social subjects - history and geography.
A more controversial aspect is to remove core skills in IT from separate computing departments and incorporate it in other subjects, such as mathematics, and set up team teaching. Drama may also be offered along with other subjects while art, music and drama may be rotated in blocks, either over terms or over the two years.
Schools have been invited to experiment with rotating other subjects to increase the amount of time pupils spend with individual teachers. Home economics and technology could be twinned, as might history and geography.
The options include studying one subject throughout S1 and another in S2, or one subject for about 19 weeks at a time or one subject for six weeks.
Schools will be free to choose different approaches. "This is a hearts and minds issue," Mr Anderson said.
John Fyffe, assistant rector at Monifieth High, and a member of the Angus S1-S2 working group, said it would be possible in two years to cut the tally of 14 teachers in S1 and 13 in S2 to 12 and 11 "without much pain".
Drama is already taught as part of English in a 10-week block. "It is not a separate subject with a separate teacher and we can afford an opportunity to team teach," Mr Fyffe said.
He favours rotated courses and cross-curricular timetabling. As a technical teacher, he would prefer more regular contact.
"If you have four first-year classes for 50 minutes each week and two classes on a Friday and Monday, then you do not get to know them as well because of in-service days, holidays and so on. If you have them for three periods a week, you build up more knowledge," Mr Fyffe said.
Angus also wants the primary 7 model of only one teacher "critically reviewed". Science or modern language specialists might work with primary classes. At the same time visiting expressive arts teachers from a primary cluster might be redeployed to the local secondary.