A form of full-potential multiple-scattering theory for electrons in solids or molecules has recently been proposed in which the structure constants characteristic of standard theory (Korringa-Kohn-Rostoker) do not occur. This formalism was derived from the Lippmann-Schwinger integral equation and has been called the Green-function cellular method. It is shown here that this formalism is a restatement of the tail-cancellation condition of Andersen, applied originally in the context of his muffin-tin-orbital construction, using a local spherical approximation to the potential function in the Schrödinger equation. This was generalized to the atomic-cell orbital (ACO) construction for the full-potential problem by the present author. The equations of this method are derived here directly from the ACO tail-cancellation condition for boundary matching on the surface of each cell in a set of space-filling atomic cells, making no use of the free-particle or Helmholtz Green function. It is also shown here that these equations correspond to a restricted variation of trial functions on the surfaces of atomic cells in the context of the variational cellular method of Leite and collaborators, derived from the variational principle of Schlosser and Marcus. © 1992 The American Physical Society.