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This contribution reconstructs the first attempt towards a critical revision of Ptolemy’s astronomical data, which took place in the school of Alexandria in the first half of the sixth century AD. The article challenges the generally accepted picture of late antique astronomy as one of blind compliance to Ptolemy’s authority, showing on the contrary the existence of criticisms and corrections. Although no systematic revision of Ptolemy’s model and methods was carried out at this time, late antique astronomers recognised the existence of several problems with his numerical data, and began a campaign of astronomical observations in order to correct them. A better understanding of this stage of scientific thought also allows to contextualise the beginnings of Arabic astronomy within a wider historical perspective: the rather free relation of Arab astronomers to Ptolemy’s authority can be understood as deriving from developments which had already started within Greek science. The article includes an edition of Ptolemy’s Table of the distances of the fixed stars, based on the four oldest extant manuscripts, dating from the ninth and tenth century. A proper critical edition would of course require a close examination of all the extant manuscripts and the elaboration of a stemma codicum, a goal which could be achieved only through a comprehensive study of the Handy Tables as a whole. However, I believe this preliminary work is already a considerable improvement to the old and unreliable edition by Nicolas Halma (1822-1825), which scholars had to use until now.