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Static soliton states in twin-core nonlinear optical fibers are examined using an improved variational approximation: the soliton’s width is an additional varying parameter, together with the ratio of the energies in, and the phase difference between, the two cores. For the symmetric coupler, results agree well with numerical ones; in particular, the bifurcation between symmetric and asymmetric solitons is shown to be slightly subcritical. For the asymmetric coupler, the control parameters are the difference between the cores’ dispersion coefficients and the phase velocity mismatch. Soliton states in the asymmetric coupler show a strong and easily controlled bistability. The soliton exists for some energies even when one of the cores has normal dispersion.