Summary: We establish some new results about the \(\Gamma\)-limit, with respect to the \(L^1\)-topology, of two different (but related) phase-field approximations \(\{\mathcal{E}_{\varepsilon}\}_{\varepsilon},\,\{\tilde{\mathcal{E}}_{\varepsilon}\}_{\varepsilon}\) of the so-called Euler’s Elastica Bending Energy for curves in the plane. In particular, we characterize the \(\Gamma\)-limit as \(\varepsilon\to 0\) of \(\mathcal{E}_{\varepsilon}\), and show that in general the \(\Gamma\)-limits of \(\mathcal{E}_{\varepsilon}\) and \(\tilde{\mathcal{E}}_{\varepsilon}\) do not coincide on indicator functions of sets with non-smooth boundary. More precisely, we show that the domain of the \(\Gamma\)-limit of \(\tilde{\mathcal{E}}_{\varepsilon}\) strictly contains the domain of the \(\Gamma\)-limit of \(\mathcal{E}_{\varepsilon}\).