Summary: We consider boundary value problems for the elliptic sine-Gordon equation posed in the half plane \(y > 0\). This problem was considered in [E. S. Gutshabash and V. D. Lipovskiĭ, J. Math. Sci., New York 68, No.2, 197-201 (1994); translation from Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 180, 53-62 (1990; Zbl 0792.35132)] using the classical inverse scattering transform approach. Given the limitations of this approach, the results obtained rely on a nonlinear constraint on the spectral data derived heuristically by analogy with the linearized case.We revisit the analysis of such problems using a recent generalization of the inverse scattering transform known as the Fokas method, and show that the nonlinear constraint of Gutshabash and Lipovskiĭ [loc. cit.] is a consequence of the so-called global relation. We also show that this relation implies a stronger constraint on the spectral data, and in particular that no choice of boundary conditions can be associated with a decaying (possibly mod \(2\pi \)) solution analogous to the pure soliton solutions of the usual, time-dependent sine-Gordon equation.We also briefly indicate how, in contrast to the evolutionary case, the elliptic sine-Gordon equation posed in the half plane does not admit linearisable boundary conditions.