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A search is ongoing for compressed gas insulants of comparable performance with sulphur hexafluoride, which will avoid its severe global warming potential. This work will be assisted by a generic understanding of the factors that limit the high voltage withstanding strength of compressed gases. Most available experimental data relate to high-pressure SF6 breakdown, but no quantitative physical model for breakdown voltage prediction has been developed other than empirical algorithms. The paper shows that a new form of the classical Paschen law can account for these data, which will provide a useful guide for the economical testing of candidate insulants and for the general design and physical limitations of equipment using compressed gases. The paper also examines the transient changes in compressible gas density that arise from shock wave development, which may influence high-pressure breakdown and determine the breakdown voltage.