The COBRA experiment aims to search for neutrinoless double beta decay (0νββ-decay) as a probe to new physics beyond the standard model. The aim of this thesis is to work towards creating a low background environment for the COBRA experiment as well as optimising and simplifying as far as possible the way in which the COBRA experiment could be operated. Several new results have been obtained. Experimental work on CZT detector operation revealed simplified ways for detector operation which would benefit a full COBRA experimental setup in terms of performance and cost. Detailed Monte-Carlo simulation studies into shielding design for COBRA aiming at a complete background model for detector design have also been undertaken and partly completed, yielding results which could also be useful for general low background applications. Finally, general data analysis methods have been developed and employed, again targeting general detector design in order to establish a blind analysis technique for COBRA.