The Headmasters' and Headmistresses' Conference, to give it its full title, represents heads of some 250 boys' and mixed-sex public schools.
It is sharing its building (views over open country, easy road and rail access) with two other private schools' bodies, the less grand Society of Headmasters and Headmistresses of Independent Schools (SHMIS) and the independent schools' professional development wing (or IPD).
But not with the girls. The Girls' Schools Association has opted to stay with SHA - sorry, ASCL - at their Leicester headquarters 12 miles away.
It's much nicer in Market Harborough, say their happy country cousins.