A semiparametric model is considered where the functional of interest is a shift parameter between two curves. A surprising example is provided where two at first sight indistinguishable Gaussian priors lead to quite different behaviours of the posterior distribution of the functional of interest. This phenomenon also illustrates that a condition introduced in Castillo (2012) of the approximation of the least favourable direction by the Gaussian prior is almost necessary for the Bernstein–von Mises theorem to hold.