Direct measurements of small nuclear reaction cross sections require a low background in the signal region of interest to achieve the necessary sensitivity. We describe two complementary detector setups that have been used for studies of p, g ( ) reactions with solid targets at the Laboratory for Underground Nuclear Astrophysics (LUNA): a high-purity germanium detector and a bismuth germanate (BGO) detector. We present the effect of a customised lead shielding on the measured background spectra in the two detector setups at LUNA. We developed a model to describe the contributions of environmental and intrinsic backgrounds in the BGO detector measurements. Furthermore we present an upgrade of the data acquisition system for our BGO detector, which allows us to exploit the features of the segmented detector and overcome some of the limitations encountered in previous experiments. We conclude with a discussion on the improved sensitivity of the presented setups, and the benefits for ongoing and possible future measurements.