A criterion is given for a smoothly bounded domain D ⊂ C 2 D \subset {{\mathbf {C}}^2} to be locally extendible to a neighborhood of a point z 0 ∈ ∂ D {z_0} \in \partial D . (This result may also be formulated in terms of extension of CR functions on ∂ D \partial D .) This is related to the envelope of holomorphy of the semitubular domain \[ Ω ( Φ ) = { ( z , w ) ∈ C 2 : Re ⁡ w + r k Φ ( θ ) > 0 } , \Omega (\Phi ) = \{ (z,w) \in {{\mathbf {C}}^2}:\operatorname {Re} w + {r^k}\Phi (\theta ) > 0\} , \] where r = | z | r = |z| , θ = arg ⁡ ( z ) \theta = \arg (z) . Necessary and sufficient conditions are given for the envelope of holomorphy of Ω ( Φ ) \Omega (\Phi ) to be C 2 {{\mathbf {C}}^2} . These conditions are equivalent to the existence of a subharmonic minorant for r k Φ ( θ ) {r^k}\Phi (\theta ) .