It is emphasized that there are two inequivalent, supersymmetric extensions of Siegel's model: one with nontrivial on-shell fermions and one without. Both extensions are coupled to (1,0) supergravity and quantized consistently in a hamiltonian formalism. The quantization of these two actions allows a fully, left-right asymmetric action for the heterotic string, and an off-shell formulation of asymmetric orbifolds.