A two-parameter family of random permutations of [n] is introduced, with distribution conditionally uniform given the counts of upper and lower records. The family interpolates between two versions of Ewens' distribution. A distinguished role of the family is determined by the fact that every sequence of coherent permutations (πn,n=1,2,…) with the indicated kind of sufficiency is obtainable by randomisation of the parameters. Generating algorithms and asymptotic properties of the permutations follow from the representation via initial ranks.