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Full completion of cognitive screening tests can be problematic in the context of a stroke. Our aim was to examine the completion of various brief cognitive screens and explore reasons for untestability. Data were collected from consecutive stroke admissions (May 2016−August 2018). The cognitive assessment was attempted during the first week of admission. Patients were classified as partially untestable (≥1 test item was incomplete) and fully untestable (where assessment was not attempted, and/or no questions answered). We assessed univariate and multivariate associations of test completion with: age (years), sex, stroke severity (National Institutes of Health Stroke Scale (NIHSS)), stroke classification, pre-morbid disability (modified Rankin Scale (mRS)), previous stroke and previous dementia diagnosis. Of 703 patients admitted (mean age: 69.4), 119 (17%) were classified as fully untestable and 58 (8%) were partially untestable. The 4A-test had 100% completion and the clock-draw task had the lowest completion (533/703, 76%). Independent associations with fully untestable status had a higher NIHSS score (odds ratio (OR): 1.18, 95% CI: 1.11−1.26), higher pre-morbid mRS (OR: 1.28, 95% CI: 1.02−1.60) and pre-stroke dementia (OR: 3.35, 95% CI: 1.53−7.32). Overall, a quarter of patients were classified as untestable on the cognitive assessment, with test incompletion related to stroke and non-stroke factors. Clinicians and researchers would benefit from guidance on how to make the best use of incomplete test data.