They say it adds little motivation and can be divisive, rewarding individuals for the whole school's efforts, damaging morale and weakening team spirit. But those who have received awards take a more positive view.
The survey, by David Marsden and Stephen French, of the Centre for Economic Performance at the London School of Economics, found most other public-sector workers agreed with performance-srelated pay on principle.
Scepticism among the 2,000 heads who responded reflected the nature of schools, according to Dr Marsden, reader in industrial relations. "A head's performance depends very heavily on the co-operation of colleagues. It's much more difficult to separate individual from collective performance."
Heads and deputies tend to be the only teachers to get merit awards, which are supposed to be linked to performance reviews by governors, but their use is patchy.
Heads in deprived areas were less likely to get performance-related awards, the survey found, possibly because governors opposed in principle or because of limited resources.
Schools that did make awards often did not link them to school results, something unions particularly fear. Instead, heads were rewarded more often for fulfiling their development plans, sound financial management or simply "sustained high performance".
'What a Performance', the Centre for Economic Performance, LSE, Houghton St, London WC2A 2AE, Pounds 15.