Background Delirium is prevalent and serious, yet remains under‐recognised. Systematic screening could improve detection; however, consensus is lacking as to the best approach. Our aim was to assess the diagnostic accuracy of five simple cognitive tests in delirium screening: six‐item cognitive impairment test (6‐CIT), clock‐drawing test, spatial span forwards, months of the year backwards (MOTYB) and intersecting pentagons (IPT). Methods A cross‐sectional study was conducted. Within 36 h of admission, older medical patients were assessed for delirium using the Revised Delirium Rating Scale. They also underwent testing using the five cognitive tests outlined above. Sensitivity, specificity, positive and negative predictive values (PPV; NPV) were calculated for each method. Where appropriate, area under the receiver operating characteristic curve (AUC) was also calculated. Results Four hundred seventy patients were included, and 184 had delirium. Of the tests scored on a scale, the 6‐CIT had the highest AUC (0.876), the optimum cut‐off for delirium screening being 8/9 (sensitivity 89.9%, specificity 62.7%, NPV 91.2%, PPV 59.2%). The MOTYB, scored in a binary fashion, also performed well (sensitivity 84.6%, specificity 58.4%, NPV 87.4%, PPV 52.8). On discriminant analysis, 6‐CIT was the only test to discriminate between patients with delirium and those with dementia (without delirium), Wilks' Lambda = 0.748, p < 0.001. Conclusion The 6‐CIT measures attention, temporal orientation and short‐term memory and shows promise as a delirium screening test. This study suggests that it may also have potential in distinguishing the cognitive impairment of delirium from that of dementia in older patients. Copyright © 2016 John Wiley & Sons, Ltd.