Secondary schools in England and Wales found it easier to recruit head teachers last year, a survey suggests.
The level of re-advertisements for posts was only 25% compared with 36% two years before that.
Professor John Howson, who checks recruitment adverts annually, said problems remained in primary schools however, with 37% re-advertised.
The government said vacancies were low and stable and head teachers were being rewarded for doing challenging jobs.
Prof Howson, of Education Data Surveys, has been researcing the issue for 23 years.
'Too few'
He said the improvement in the secondary sector could be attributed to two factors.
One was a better supply position now that the effect of the introduction of the assistant head grade - absorbing a proportion of candidates - had been overcome.
The other was that school governing bodies, who carry out the recruitment, had a greater understanding of the market following a campaign by the National College for School Leadership (NCSL).
But he said it was clear that primary schools seemed to be "chasing too few candidates".
Faith schools again found it harder than did community schools, and there were record levels of difficulty in the north-west and east of England.
Prof Howson said the NCSL should explain to governors how many candidates they might expect to apply for a headship so they could make realistic decisions.
More than 2,600 schools advertised for a new head teacher for the first time during 2007: nearly 400 secondary, some 2,100 primary and 144 special schools and units.
They included more than 40 academies, mostly new ones.
Generally, schools continued to find little difficulty in recruiting new deputy or assistant head teachers.
'Out of balance'
Prof Howson also said a surge in vacancies had been expected because of the large number of older heads due to retire, but this had not appeared.
This might have been due to amalgamations and federations, he suggested, adding that 2008 might prove to be a critical year in this respect.
"Although the market for head teachers remains out of balance, most schools have fewer problems recruiting either a deputy or an assistant head teacher," Prof Howson said.
"This suggests that there is no real unwillingness to take on a leadership role."
The key question that only the NCSL could answer was whether the supply of suitably qualified trainees was sufficient to meet the demand for new head teachers amongst all the many different types of schools.
A spokesman for the Department for Children, Schools and Families said vacancies were "low and stable".
"We recognise that leading a school is a rewarding, challenging role and that is why we are paying heads in inner London up to a six-figure salary from this September."
Chris Kirk, director of succession planning at the NCSL, said it found a strong appetite among teachers to reach headship.
"NCSL has also found there is a pool of ambitious candidates for primary schools, and the challenge is matching them in the right place at the right time," he said.
It was working to match up candidates and schools and in close partnership at a local level with schools, local authorities, dioceses, governors and current heads.
But the general secretary of the National Union of Teachers, Steve Sinnott, said: "The yawning gap in primary head teacher recruitment is a symptom of teachers' belief that the job is un-doable.
"The pressures of excessive monitoring, league tables, over-prescriptive strategies are a poor advertisement for headship."
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