The Antikythera Mechanism is an extraordinarily complex ancient Greek astronomical calculating device whose mode of operation is now relatively well understood particularly since imaging studies in 2005 revealed gears and inscriptions which were previously illegible. Unfortunately, the highest resolution X-ray computed tomography image of the largest fragment had some errors which meant that the reconstructed images were not as clear as had been expected. Here, the original X-ray data have been reanalysed and reconstructed. The new X-ray computed tomography images have improved contrast and resolution, leading to better clarity and legibility. The improvement in image quality is characterised and some examples of writing on the Mechanism which can now be read with increased confidence are given.