A new type of hinging is explored for geometric dissections of two-dimensional figures. The figures are represented by pieces on two adjacent levels. Piano hinges are used to rotate a piece B from being next to a piece A on one level to being above or below piece A on another level. Techniques are presented and analyzed for designing piano-hinged dissections. These include the use of polygon structure, the conversion from twisted-hinged dissections, the folding analogue of a P-slide, the folding analogue of a step dissection, and the use of tessellations. Properties of piano-hinged dissections are explored. An open problem relating to the possible universality of such hingings is posed.