Single-neuron activity in the prefrontal cortex (PFC) is tuned to mixtures of multiple task-related aspects. Such mixed selectivity is highly heterogeneous, seemingly disordered and therefore difficult to interpret. We analysed the neural activity recorded in monkeys during an object sequence memory task to identify a role of mixed selectivity in subserving the cognitive functions ascribed to the PFC. We show that mixed selectivity neurons encode distributed information about all task-relevant aspects. Each aspect can be decoded from the population of neurons even when single-cell selectivity to that aspect is eliminated. Moreover, mixed selectivity offers a significant computational advantage over specialized responses in terms of the repertoire of input–output functions implementable by readout neurons. This advantage originates from the highly diverse nonlinear selectivity to mixtures of task-relevant variables, a signature of high-dimensional neural representations. Crucially, this dimensionality is predictive of animal behaviour as it collapses in error trials. Our findings recommend a shift of focus for future studies from neurons that have easily interpretable response tuning to the widely observed, but rarely analysed, mixed selectivity neurons. When an animal is performing a cognitive task, individual neurons in the prefrontal cortex show a mixture of responses that is often difficult to decipher and interpret; here new computational methods to decode and extract rich sets of information from these neural responses are revealed and demonstrate how this mixed selectivity offers a computational advantage over specialized cells. When an animal performs a cognitive task, individual neurons in the prefrontal cortex are often 'tuned' to various aspects related to the behaviour. The resulting mixture of responses is often difficult to decipher. This study of neural activity in monkeys performing an object sequence memory task was designed to establish whether the predominance of mixed selectivity neurons in the prefrontal cortex is critical to the function being performed. The results suggest that neurons with mixed selectivity contain as much information as those that are highly specialized in encoding a single task-relevant aspect. And mixed selectivity neurons actually offer a significant computational advantage over specialized cells in some respects. The new computational methods developed for this work to extract rich sets of information from recorded neural activity should make it easier to study the widely observed but rarely analysed mixed selectivity neurons.