Algorithms are used in public management decisions, for instance, to allocate police staff to potential crime scenes. We study how the usage of algorithms for managerial decisions affects procedural justice as reported by public employees. We argue that some public management practices may be more suitable for algorithmic decision-making than others. We hypothesize that employees' perceptions differ depending on the complexity of the practice at hand. We test this through two survey experiments on 109 Dutch public employees and 126 public employees from the UK. Our results show that when a decision is made by an algorithm for practices that are low in complexity, procedural justice increases. Our results also show that, for practices that are high in complexity, decisions involving a public manager are perceived as higher in procedural justice compared to decisions that were made automatically by computers using algorithms. Nevertheless, adding an algorithm to a public manager's decision-making process can increase procedural justice for high complexity practices. We conclude that managers should explore automation opportunities for low complexity practices, but to be cautious when using algorithms to replace public managers' decisions for high complexity practices. In the latter case, transparency about algorithms and open dialogues on perceptions could be beneficial, but this should not be seen as a panacea. •Using algorithms for managerial decisions can affect employees' procedural justice•Effects depend on complexity and are largest when algorithms are automated•For low complexity practices, including algorithms increases procedural justice•For high complexity practices, automating algorithms decreases procedural justice