In an earlier paper by the authors (Peale and Boss, 1977), rather severe constraints were placed on the properties of a Mercurian liquid core and certain other dynamical characteristics of the planet for consistency with Mercury's escape from the spin-orbit resonance with the spin angular velocity equal to twice the orbital mean motion. One assumption under which these constraints were established was that the obliquity ϑ?0 at the time of resonance passage. Here we show that for ϑ≠0. Mercury can easily escape the spin resonance with a large core of low viscosity, and all constraints established for resonance passage for ϑ=0 would vanish. However, the same effect which so drastically reduces the probability of capture into the 2n resonance also would have reduced ϑ to negligibly small values long before the 2n resonance was reached. Thus Mercury most likely passed through &psgr;iM=2n with ϑ?0, and hence the previously established constraints of the kinematic viscosity v?0.01 and the tidal dissipation factor Q≲100 for a laminar core-mantle boundary layer and the constraints on critical Reynolds number Ric>500, tidal Q≲40, and moment differences (B--A)/C≲10-5 for a turbulent boundary layer are still applicable for any core capable of dynamo generation of a magnetic field.