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An individual's h-index corresponds to the number h of his/her papers that each has at least h citations. When the citation count of an article exceeds h, however, as is the case for the hundreds or even thousands of citations that accompany the most highly cited papers, no additional credit is given (these citations falling outside the so-called “Durfee square”). We propose a new bibliometric index, the “tapered h-index” (hT), that positively enumerates all citations, yet scoring them on an equitable basis with h.The career progression of hT and h are compared for six eminent scientists in contrasting fields. Calculated hT for year 2006 ranged between 44.32 and 72.03, with a corresponding range in h of 26 to 44. We argue that the hT-index is superior to h, both theoretically (it scores all citations), and because it shows smooth increases from year to year as compared with the irregular jumps seen in h. Conversely, the original h-index has the benefit of being conceptually easy to visualise. Qualitatively, the two indices show remarkable similarity (they are closely correlated), such that either can be applied with confidence.