But, interviewed by The TESS, they said the post would be much more attractive if there was a clearer pathway to it, better continuing professional development and a bigger pay differential.
A long-awaited report into headteacher recruitment and retention, published last week by the Scottish Government, pointed to a growing leadership crisis for schools as it found that only 8 per cent of teachers aspired to a headship.
Kathryn Dalrymple, depute head of Tulloch Primary in Perth, said two years ago, the headteacher of her school earned only pound;1,800 more than she did (although the post has since been job-sized differently).
For a salary differential of less than pound;2,000, it was "not worth the hassle" taking on the responsibilities of being a head, said Ms Dalrymple, who also serves as deputes' representative on the AHDS national executive committee.
She added: "The best thing about being a depute is that you're in the middle between the staff and the headteacher. I have got someone to fall back on and I have also got autonomy to make decisions but, at the end of the day, the buck stops with the headteacher."
Gordon Smith, former headteacher of Jordanhill Primary in Glasgow, said he wanted to see a Scottish equivalent of England's National College for School Leadership - an institution that would deliver the training and CPD on which he felt many heads had missed out.
He said it could be run under the auspices of the General Teaching Council for Scotland and provide clearer opportunities for promotion, offering secondments and other training opportunities. "Continuing professional development provision for headteachers just now is abysmal," Mr Smith declared.
Bill Milligan, head of Dalmilling Primary in South Ayrshire and AHDS professional advice convener, attributed the dramatic drop in the number of applications for headteacher posts to the lack of financial incentives for what was a "lonely job".
He added: "I have colleagues who support me tremendously well and I have an exemplary team, but they won't get it in the neck if something goes wrong - I will."
Mr Milligan echoed some of the findings of the report - that headteachers identified accountability to HMIE and local authorities, along with bureaucracy, as reasons for not recommending the job to other people.
"I worry that I am not producing the quality either that I am capable of or could do if the job was less onerous," he said.
"Often, it is the minutiae that take you away from the learning and teaching in the school."