The authors prove that all n-th completely bounded cohomology groups of a nest algebra T(N) acting on a separable Hilbert space are trivial when the coefficients lie in any ultraweakly closed T(N)-bimodule containing the nest algebra. They also prove that Hcnb(A, M) (≌) Hcnb(A, A) for all n ≥ 1 and a CSL algebra A with an ultraweakly closed A-bimodule M containing A.