All cortical areas are characterised by a fundamental division of labour between neurons: principal (or projection) neurons project to other brain areas, whereas the influence of interneurons remains local. Thus, information about the activity of interneurons is lost in downstream areas, yet, their activity seems crucial for proper functioning. What principles govern the functional role of interneurons? We explored this question in the context of attractor dynamics, a paradigmatic model of cortical computation. Using techniques that we have recently developed to embed multiple robust attractors in realistic neural networks by optimising their synaptic weights [Festa et al., NIPS 2014], we found that interneurons are crucial for achieving high capacity. We studied a progression of models with increasing biological realism, ranging from neurons with saturating input/output gain functions and no distinct excitatory/inhibitory (E/I) identity (standard dynamic Hopfield scenario), to distinct E/I neurons with expanding gain functions that do not saturate over the relevant dynamic range. We distinguished between principal and interneurons based on whether their activities were pre-specified by the attractors or could freely vary throughout optimisation. Our optimisation procedure reproduced the well-known high capacity of the Hopfield network without interneurons when trained with the perceptron rule. However, interneurons became crucial for the robust stabilisation of attractor states when neurons had non-saturating gain functions. In particular, the strategy used by capacity-optimised circuits was to use interneurons to “index” memories, such that they exhibited a number of unique, experimentally testable features in their connectivity and their dynamics.