It is urging the Scottish Office to acknowledge the consequences of giving schools discretion in allowing pupils to sit Standard grade and Higher exams a year earlier. Exemption from existing "age and stage restrictions" requires specific approval from the Scottish Qualifications Authority for each exam candidate.
Angus MacDonald, Inverclyde's head of support for learning, described the consultation document as "lightweight".
"This paper has considerable implications for schools, yet the issues it raises are not adequately thought through or dealt with. Schools that are already magnet schools could find themselves under pressure to bypass Standard grade for the ablest," Mr MacDonald said.
"This in turn will reinforce the flight of middle-class parents from other schools that don't have sufficient numbers to run Standard grade and Higher Still courses in the third and fourth years."
In its official response, Inverclyde says the best strategy from a management point of view "would be to have Higher Still progress on directly from 5-14 at the appropriate level, with each pupil progressing at his or her own speed. "
Glasgow's submission also raises the spectre of the disappearance of Standard grade, "in the light of pressure to improve achievement in S1-S2 and in view of the advent of Higher Still".
The addition of a sixth level F to the 5-14 curriculum, together with Access and Intermediate courses as sub-Higher levels of the Higher Still programme, is seen as potentially squeezing out Standard grade. But the fourth-year exam will be strongly defended by the unions, partly because of the teacher effort invested in its development but also because they fear a slide towards streaming.
Glasgow's acceptance of accelerated Standard grade presentation in S3 and Higher in S4 is conditional on restricting it to the very ablest pupils.
The council, however, says the current Standard grade programme has serious weaknesses.