Using many-body perturbation theory within the G0W0 approximation, we explore routes for computing the ionization potential (IP), electron affinity (EA), and fundamental gap of three gasphase molecules -benzene, thiophene, and (1,4) diamino-benzene -and compare with experiments.We examine the dependence of the IP on the number of unoccupied states used to build the dielectric function and the self energy, as well as the dielectric function plane-wave cutoff. We find that with an effective completion strategy for approximating the unoccupied subspace, and a converged dielectric function kinetic energy cutoff, the computed IPs and EAs are in excellent quantitative agreement with available experiment (within 0.2 eV), indicating that a one-shot G0W0 approach can be very accurate for calculating addition/removal energies of small organic molecules. Our results indicate that a sufficient dielectric function kinetic energy cutoff may be the limiting step for a wide application of G0W0 to larger organic systems. arXiv:1204.0509v1 [cond-mat.mtrl-sci]