The authors prove that all n-th completely bounded cohomology groups of a nest algebra $T({\cal N})$ acting on a separable Hilbert space are trivial when the coefficients lie in any ultraweakly closed $T({\cal N})$-bimodule
containing the nest algebra. They also prove that $H_{cb}^n({\cal A},{\cal M})\cong H_{cb}^n({\cal A},{\cal A})$ for all $n\geq 1$ and a CSL algebra ${\cal A}$ with an ultraweakly closed ${\cal A}$-bimodule ${\cal M}$ containing ${\cal A}$.