The revamped vice-chancellors' representative body got off to a bumpy start with a disagreement between policy chiefs and Scottish university and college heads.
Members of the Committee of Scottish Higher Education Principals, which has retained its autonomy while agreeing to join the new devolution-friendly Committee of Vice-Chancellors and Principals, fell out with CVCP officials over submissions to the Cubie inquiry into student tuition fees in Scotland.
They were furious that, despite pledges to maintain good lines of communication between the two organisations, the CVCP posted its submission without sharing its contents with Coshep.
They were even more angry to find that the CVCP submission appeared to be an attempt to "bounce" Coshep into holding a "United Kingdom line" over fees.
The CVCP paper, in the form of a letter from committee chief executive Diana Warwick, warned against funding changes in one part of the UK that would lead to "major anomalies" elsewhere.
But while the Coshep submission stressed the importance of students making a means-tested contribution towards tuition, it also suggested that in Scotland this might be paid on students' behalf and recovered once they were earning, rather than being paid up-front.
It also suggested non-repayable bursaries for poorer students and higher loans.
Baroness Warwick said the CVCP had been "very pleased" with the Coshep submission. It felt that its own paper "made sure that Cubie understood the wider perspective in England, Wales and Northern Ireland".
This week Coshep convener Ian Graham-Bryce, principal of Dundee University, admitted there had been a "vigorous interaction" with the CVCP.
He played down the disagreement, however, describing it as "a teething trouble" in the formation of the restructured CVCP.
He said: "In respect of the actual submissions, there was a little bit of a glitch in that the CVCP one went in without our seeing it."
But he added: "It was accepted by CVCP that Coshep would be the lead body. The CVCP submission differs from Coshep in that they were arguing for options to be left open, whereas we were more specific. But it's not in any fundamental respect different."
Both Coshep and the CVCP appear to have agreed to put the row behind them.
A Coshep spokesman said: "The specific incidents around the Cubie submission are well and truly in the past."
A CVCP spokeswoman said: "It's not a bone of contention at present."
Dr Graham-Bryce said: "The organisation is still very new, and it's hardly surprising that we are all learning how to operate it."