Fife expressed concern at the affect the emphasis on language and maths would have in primary schools.
Angus Council singled out for criticism the use of the free meals uptake to establish targets.
The council had "very serious concerns about the credibility of any targets derived from this single indicator. First impressions of its impact on the provisional targets set tend to exacerbate these concerns."
All three authorities call for teachers to receive training. This is particularly important in primaries which have not accumulated the same experience as secondaries in analysing exam performance.
North Lanarkshire says schools will need advice and support in order to "discourage teaching to the test, improve attainment and promote the full development of all pupils". The council's own strategy for raising achievement includes pupils' social, artistic and sporting prowess, not just academic attainment.
But Fife fears that the school characteristics index derived from free meals will not be acceptable unless it includes a measure of pupils' prior attainment. North Lanarkshire also stresses the importance of establishing "credible, consistent and reliable baseline measures of assessment".
Angus complains about the "extraordinarily short" time scale before the authorities have to submit agreed targets to the Scottish Office. "It is vital that, if the exercise is to have any credibility, the targets are realistic, stretching and attainable.
"Early impressions suggest very strongly that not all the targets will meet these criteria ... It is therefore necessary to ensure that full consideration is given to all relevant factors before the final targets are submitted."
Fife concludes nonetheless that, despite the criticisms, "it would be very easy to engage in discussions about the technical merits of the approach proposed ... It is clear that it can be linked to existing structure and processes. It can help focus attention."
North Lanarkshire says only time will tell whether the target-setting system "has the sensitivity and refinement necessary to deliver its declared aim of raising standards of attainment".