Neurites avoid overlapping with sister-neurites, stemming from the same neuron, while simultaneously overlapping freely with different neurons; an ability that is integral to neural circuit assembly in both vertebrates and invertebrates. Counterintuitively, in this process, interactions between cell surface proteins drive neurite repulsion rather than adhesion. In the vertebrate brain, self-avoidance is mediated by stochastic expression of distinct combinations of ~60 clustered protocadherins. Surprisingly, in the substantially smaller Drosophila brain, an analogous function is mediated by a significantly larger family of approximately 36,000 proteins. The underlying molecular mechanism that allows only ~60 proteins, in the mammal brain, to provide sufficient diversity to support self-avoidance within this larger and more complex brain remains unclear. I will present results that have led us to suggest a molecular mechanism for self-vs-non-self-discrimination among vertebrate neurons.