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Inter-time (i.e., the time that separates a PD event from the next one) distribution analysis has been recently proposed as a tool to infer the presence of trees in solid insulation systems. In this paper, inter-time distribution analysis is improved to infer more accurately trees at an early growth stage. Measurements from both artificial specimens as well as practical objects are presented to support the effectiveness of this tool. Moreover, considerations on inter-time analysis robustness with respect to both noise interference and other partial discharge sources are reported.