We undertake a detailed investigation of the morphology of YBCO step-edge junctions on MgO substrates using a range of techniques. Differences between the grain boundary structure of step-edge junctions and other more commonly studied [001]-tilt junctions, including good atomic alignment across a ~ 1 nm wide grain boundary and less lattice mismatch and faceting, are highlighted. Transport measurements reveal high <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">IcRn</i> products over a large range of critical current densities, <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Jc</i> , and a slower reduction in <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Jc</i> as the step angle increases, compared with [001]-tilt junctions.