This paper studies finite spectrum assignment for linear scalar systems with non-commensurate time-delays based on a practically important class of finite Laplace transforms. The finite spectrum assignability can be reduced to the solvability of a Bezout equation over a multivariable polynomial ring with coefficients in the class of finite Laplace transforms. It is shown that, in the non-commensurate delay case, spectral canonicity is not sufficient for the finite spectrum assignability.