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This paper summarizes the research carried out to investigate the dependence of the strength of external insulation on air density, with particular reference to positive polarity impulses, generally of major interest for design and testing.New tests were carried out up to an altitude of about 3000 m a.s.l., with particular attention to the influence of air density on the strength and on the discharge process.It was found that, for positive switching impulses, the variation of the breakdown voltage with air density is more marked at lower density values. This trend is not fully taken into account by current correction methods.A refined correction approach is proposed to account for the above mentioned aspects, with special attention to high altitudes.