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Given the urgent need to devise credible, deep strategies for carbon neutrality, approaches for `modelling to generate alternatives' (MGA) are gaining popularity in the energy sector. Yet, MGA faces limitations when applied to state-of-the-art energy system models: the number of alternatives that can be generated is virtually infinite; no realistic computational effort can discover the complete technology and spatial diversity. Here, based on our own SPORES method, a highly customisable and spatially-explicit advancement of MGA, we empirically test different search strategies - including some adapted from other MGA approaches - with the aim of identifying how to minimise redundant computation. With application to a model of the European power system, we show that, for a fixed number of generated alternatives, there is a clear trade-off in making use of the available computational power to unveil technology versus spatial diversity of system configurations. Moreover, we show that focussing on technology diversity may fail to identify system configurations that appeal to real-world stakeholders, such as those in which capacity is more spread out at the local scale. Based on this evidence that no feasible alternative can be deemed redundant a priori, we propose to initially search for options in a way that balances spatial and technology diversity; this can be achieved by combining the strengths of two different strategies. The resulting solution space can then be refined based on the feedback of stakeholders. More generally, we propose the adoption of ad-hoc MGA sensitivity analyses, targeted at testing a study's central claims, as a computationally inexpensive standard to improve the quality of energy modelling analyses.