Distilling highly entangled quantum states from weaker ones is a process that is crucial for efficient and long-distance quantum communication and has implications for several other quantum information protocols. We introduce the notion of distillation under limited resources and specifically focus on the energy constraint. The corresponding protocol, which we call the canonical distillation of entanglement, naturally leads to the set of canonically distillable states. We show that for non-interacting Hamiltonians, almost no states are canonically distillable, while the situation can be drastically different for interacting ones. Several paradigmatic Hamiltonians are considered for bipartite as well as multipartite canonical distillability. The results have potential applications for practical quantum communication devices.