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According to the Parasuraman‐Berry‐Zeithaml conjecture, the greater the importance of a given quality dimension, the thinner the corresponding tolerance zone would be. This paper seeks to test the conjecture when attribute items are individually considered. The original data have been collected to assess the quality of postal services in Brazil. A qualitative stage yielded a list comprising 39 attribute items. In the quantitative stage the three‐column format of a SERVQUAL questionnaire was employed to permit the computation of importance weights and tolerance widths for each attribute item. The questionnaire was mailed to a sample of some 5,900 firms. About 10 per cent (540) of mailed questionnaires returned and were considered valid. The values obtained for the correlation coefficients were significantly negative and consistently close to each other. The inverse association between importance and tolerance of service quality attributes was then accepted. The most interesting consequence of this finding is that simply ordering the computed width of attributes’ zones of tolerance will yield the most important attributes. Other implications are also discussed.