Background: Report cards on the health care system increasingly report provider-specific performance on indicators that measure the quality of health care delivered. A natural reaction to the publishing of hospital-specific performance on a given indicator is to create 'league tables' that rank hospitals according to their performance. However, many indicators have been shown to have low to moderate rankability, meaning that they cannot be used to accurately rank hospitals. Our objective was to define conditions for improving the ability to rank hospitals by combining several binary indicators with low to moderate rankability. Methods: Monte Carlo simulations to examine the rankability of composite ordinal indicators created by pooling three binary indicators with low to moderate rankability. We considered scenarios in which the prevalences of the three binary indicators were 0.05, 0.10, and 0.25 and the within-hospital correlation between these indicators varied between - 0.25 and 0.90. Results: Creation of an ordinal indicator with high rankability was possible when the three component binary indicators were strongly correlated with one another (the within-hospital correlation in indicators was at least 0.5). When the binary indicators were independent or weakly correlated with one another (the within-hospital correlation in indicators was less than 0.5), the rankability of the composite ordinal indicator was often less than at least one of its binary components. The rankability of the composite indicator was most affected by the rankability of the most prevalent indicator and the magnitude of the within-hospital correlation between the indicators. Conclusions: Pooling highly-correlated binary indicators can result in a composite ordinal indicator with high rankability. Otherwise, the composite ordinal indicator may have lower rankability than some of its constituent components. It is recommended that binary indicators be combined to increase rankability only if they represent the same concept of quality of care.