Several years ago, Professor Martin Josefsson told the first-named author, in a private communication, that his ‘characterisations of’ and ‘properties of’ series of papers that comprised tangential, extangential, bicentric, orthodiagonal, equidiagonal, and bisect-diagonal quadrilaterals, and rhombi and trapezoids, did not include parallelograms because the many characterisations of these figures are well known and are easily accessed via the net, and that nothing interesting can be added. In this Article, we present some characterisations of parallelograms that are very likely unknown and that will hopefully appeal to the readers of the Gazette. Other interesting characterisations that we have obtained and that could not find their place here are intended to form the material of another Article.