After a "lively" meeting with the universities and colleges last week, Mr Woodhead signed a peace treaty with them in which he agreed to postpone the start of the primary inspections until next term (they had been due to start now) and, most significantly, to include all 68 institutions in the new inspection of primary courses, focusing on reading and number.
This will take two years and will run concurrently with the inspection of secondary teacher training, which has just started.
The primary courses will keep the gradings they were given by Her Majesty's Inspectorate in the original inspection, but additional grades for reading and number will be added.
Opinion, however, is divided among teacher trainers over whether this really represents a climbdown on Mr Woodhead's part or whether he actually wanted to blitz all the institutions again in the first place.
Another question exercising the universities is the fact that the new framework for initial teacher training inspection - published this week - is due to be changedagain next September, yet the inspection programme will last for two years.
"Will some courses be inspected under one set of criteria and some another?" asked one principal.
The decision to single out 20 institutions for a tightly focused scrutiny of literacy and numeracy was announced by Mr Woodhead in June after the inspectorate's damning report on literacy in three inner-London boroughs focused attention on teacher training.
The move provoked outrage among the institutions selected. They claimed it was unfair and legally questionable, and some of them threatened to resist the revisit by withdrawing co-operation.
The decision also irritated HM inspectors who had worked on the primary sweep; they saw it as a slur on their professional competence.
In a letter, dated November 20, sent to all institutions after the meeting, Mr Woodhead sets out a "slightly modified plan of action".
The primary inspection programme for 1997 is intended, he says, "to help us contribute to the national curriculum for ITT which is likely to be in place by September 1997".
After that, the national curriculum itself will provide the basis for inspections.
Peter Mortimore, director of the London Institute of Education, told The TES he could not see the sense in inspecting all primary courses when the framework for inspection would be changing again next September.
Professor Mortimore was infuriated by Mr Woodhead's inclusion of the London institute on the "hit list" because it had received top grades from OFSTED the first time round, and, says Professor Mortimore, HMI did thoroughly examine students' competence in reading and number.
The latest ITT inspection framework, published on Tuesday, has again changed the definition of grade 3, "sound". Grade 3 now means "adequate, but requires significant improvement" - but getting a grade 3 will not affect funding of the course.
In his letter, the chief inspector also stresses that OFSTED will not be inspecting the partner schools. "The only circumstances in which a report might be made about a school itself would be where inspectors discovered serious problems I such as a danger to the health and safety of pupils, such that it would be a dereliction of duty not to report upon it."
School staff and teacher unions had been concerned that the primary training reinspection might involve them in "double jeopardy" OFSTED inspections.
He also says that OFSTED is developing "detailed instruments" for the scrutiny of reading and number to supplement the latest framework, published on Tuesday.
Meetings to discuss these will be arranged before the end of this term. OFSTED still plans to publish a report on the original primary sweep before Christmas.
Patricia Ambrose, policy adviser at the Committee of Vice-Chancellors and Principals, said the universities welcomed the compromise, although they had wanted to postpone the whole thing for a year.
The CVCP was, however, taking legal advice over the Secretary of State's freedom to dictate the content of teacher training courses via the proposed national curriculum, she said.
The universities argue that both the 1992 FE and HE Funding Act and the 1994 Education Act outlaw this.
Ms Ambrose also raised the issue of cost: universities would have to pay an estimated Pounds 25,000 each towards the primary inspections next year (a total of Pounds 1.7 million), quite apart from OFSTED's own costs.
Ian Kane, chairman of the Universities Council for the Education of Teachers, said the real worry was how the Teacher Training Agency used the information gleaned by OFSTED, and how funding was allocated.
"Let's see the TTA's books," he said.