The background of a coaxial Ge detector placed at a surface laboratory has been reduced by means of a background reduction setup consisting of a passive shield of low-activity lead, a simple radon suppression system and an active shield with a plastic scintillation plate. In particular, we have devoted our efforts to in-depth optimization of each parameter associated with different anticoincidence setups and to their subsequent intercomparison. The overall performance of the active shield was improved by using the optimum time parameters for each setup. The final objective is to decrease the cosmic-ray background and, by this way, to reduce the detection limits of gamma-ray spectrometers at conventional laboratories, and consequently make them competitive for different measurements like (210)Pb dating.