We adapt the strong-coupling method first used in the one-channel Kondo model to develop a simple description of the spin-1/2 two-channel Kondo model with channel anisotropy. Our method exploits spin-charge decoupling to develop a compactified Hamiltonian that describes the spin excitations. The structure of the fixed-point Hamiltonian and quasiparticle impurity S matrix are incompatible with a Fermi-liquid description.