We improve on Fourier transforms (FT) between imaginary time $τ$ and imaginary frequency $ω_n$ used in quantum cluster approaches. The asymptotic behavior of the electron Green's function can be improved by using a ``sumrule'' boundary condition for a spline. For response functions a two-dimensional FT of a singular function is required. We show how this can be done efficiently by splitting off a one-dimensional part containing the singularity and by performing a semi-analytical FT for the remaining more innocent two-dimensional part. Comment: 4 pages, 3 figures, submitted to the Brief Reports section of Phys. Rev. B