In order to reliably estimate the rate of a charged particle induced nuclear reaction in a non-explosive astrophysical scenario, its cross-section must be measured far below the Coulomb barrier. However, at the corresponding energies the cross-section values are very low, so that the experimental counting rate is dominated by cosmic-ray induced background, even if a suitable anticoincidence shield is applied. This problem can be overcome by performing an accelerator-based experiment in a deep underground site, as has been done with great success at the LUNA 0.4MV accelerator in Gran Sasso, Italy. Several underground accelerators with higher beam energy are in the planning phase worldwide. All of them are shielded by over 1000m of rock, a depth at which cosmic-ray effects are negligible for the purposes of nuclear astrophysics experiments. It is shown here that a combined approach, using a shallow-underground laboratory below 47m of rock and an active shield to veto surviving muons in simple detectors, results in a background level that is not far from that of deep underground sites. Data have been obtained using two "traveling" gamma-detectors. They have been transported both shallow underground, to the Dresden Felsenkeller in Germany, and deep underground, to the Gran Sasso laboratory in Italy. As shallow-underground facilities are more easily accessible than deep-underground ones, the present finding holds the promise of greatly accelerated progress in the field of cross-section measurements for nuclear astrophysics.