Norm-closed bimodules of nest algebras

Let {dollar}{lcub}cal N{rcub}{dollar} be a complete nest in a separable Hilbert space H, and let {dollar}alg{lcub}cal N{rcub}{dollar} be the nest algebra related to {dollar}{lcub}cal N{rcub}{dollar}. We obtain necessary and sufficient conditions for {dollar}{lcub}cal B{rcub}{dollar}(H) to be principally generated as a norm-closed bimodule of {dollar}alg{lcub}cal N{rcub}{dollar}. The same conditions characterize when {dollar}{lcub}cal B{rcub}{dollar}(H) is principally generated as a norm-closed bi-module of the quasitriangular algebra {dollar}alg{lcub}cal N{rcub}{dollar} + {dollar}{lcub}cal K{rcub}{dollar}, and when the Calkin algebra is principally generated as a norm-closed bimodule of the image of {dollar}alg{lcub}cal N{rcub}{dollar} under the Calkin homomorphism. In each case countable generation is equivalent to principal generation.