Demand-aware communication networks are networks whose topology is optimized toward the traffic they need to serve. These networks have recently been enabled by novel optical communication technologies and are investigated intensively in the context of datacenters. In this work, we consider networks with one of the most common topologies~ -- a binary tree. We show that finding an optimal demand-aware binary tree network is NP-hard. Then, we propose optimization algorithms that generate efficient binary tree networks on real-life and synthetic workloads.