In this talk I will look at the role of observational scrupulosity in the astronomical manuscripts of Thomas Harriot (1560-1621) relating to his telescopic observations of the moon, sun-spots, the moons of Jupiter and the 1618 comet. I will reflect on his interest in the observations of Tycho Brahe, and Brahe’s attempts to make his observations and measurements more accurate (particularly his computational tables regarding the ‘leges refractionum’ which aimed to quantify the differences between the real and apparent positions of celestial objects). I will pay particular attention to Harriot’s unpublished (and unfinished) treatise ‘Thomae Harrioti Collectio et comparatio quorundam obseruationum quae putabuntur accuratissimae, quia factae magnis instrumentis et a praestantibus Mathematicis: vt inde iudicium fiat de obseruationum certitudine in genere; et an vlla praestare possit ad minutum’ [By Thomas Harriot. A Collection and Comparison of certain observations, which are considered to be most accurate, because they were made using large instruments and by famous Mathematicians: so that from hence a judgement might be made of the certainty of observations in general; and whether any of them can be done better to the minute] and the criticisms which Harriot offers of the astronomical observations of Tycho and his colleagues, and aim to show the role which accurate computation played in his own astronomical work.