More than half, 52 per cent were "very satisfied" with the shorter, more frequent visits introduced from September 2005. Another 36 per cent said they were "quite satisfied", with one in ten "not satisfied at all", the National Foundation for Educational Research study found.
But there was concern from more than half of schools about the time it took to complete the self-evaluation forms before inspections. And more than a quarter of the schools were unhappy about Ofsted's use and interpretation of data, which the new system is more reliant on.
One said: "There should be less emphasis on data crunching and more understanding of the issues."
The research was used to compile Ofsted's own evaluation of its work, also published today.
Since initial teacher training providers began to be inspected in 1994, most had moved to a position where their courses were good or better.
Schools in special measures were improving more rapidly than before and inspection had also increased the proportion of good independent schools, childminders and daycare providers. The foundation's study is based on the views of 1,597 schools inspected between October 2005 to March 2006 and found the new inspection framework was "generally perceived as contributing to school improvements."
There was dissatisfaction in schools over the words used for overall gradings, particularly the "satisfactory" rating. Some schools felt the terms were "too negative and too rigid".
A poll of pupils commissioned by Ofsted found that only half whose schools were inspected under the new framework remembered receiving the letters sent to them reporting the findings. Only two thirds found them helpful.
The Ipsos Mori survey of 2,332 pupils found that 70 per cent were in favour of school inspections.
Despite concern over the time taken to fill in forms there was a "strong view" that self-evaluation was an effective way of identifying strengths and weaknesses.
Two thirds of schools reported no difference between grades they had awarded themselves and those from their inspections. The research found that the longer the new framework was in operation, the "more in tune" the grades became. Two thirds of schools said their inspections contributed to school improvements.