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In the present paper, the authors, long since engaged in research about fatigue effects of crane mechanical oscillations, after a detailed criticism of existing procedures, draft European Standard prEN 13001-1 included, propose a simple and rigorous methodology for random fatigue strength verifications. The authors decided to publish this paper because they realised that some crane companies had begun to exalt, in commercial notices and on line, the accomplishment of the not yet official and, indeed, still incomplete prEN 13001-1. As an advantageous alternative, two equivalent methods, strictly complying with the cumulated damage Miner's rule, are proposed, which could be considered two "allotropic" forms of a single algorithm. The proposed procedures, particularly dedicated to mechanisms submitted to stress histories with low stresses at high cycle numbers, could be extended to different applications. For comparison purposes, two examples are recommended to the reader's attention: the first is derived from E 1049-97 ASTM Standard, the second from crane construction experience.