An analysis of two-dimensional scattering from a narrow groove in an impedance plane is presented. The groove is represented by an impedance surface and hence the problem reduces to that of scattering from an impedance strip in an otherwise uniform impedance plane. On the basis of this model, appropriate integral equations are constructed using a form of the impedance plane Green's functions involving rapidly convergent integrals. The integral equations are solved by introducing a single-basis representation of the equivalent current on the narrow impedance insert. Both transverse electric and transverse magnetic polarizations are treated. The resulting solution is validated by comparison with results from the standard boundary integral method and a high-frequency solution. It is found that the presented solution for narrow impedance inserts can be used in conjunction with the high-frequency solution for the characterization of impedance inserts of any given width.