I'm waiting for semprecapelli to give me some more details about the manufacturing process.
But my understanding by looking at my pieces is that the flat lace is given its curvature by using thin stitching in rings of concentric circles (smallest in the middle of the piece fanning outwards) with ever increasing, minuscule tension adjustment.
This gives the piece its contour.
Obviously its a more time consuming method than crude pleats but I thought it was now standard.
There seems little point in developing finer base materials if, at some point, its being doubled up to create a pleat.
Failing that, I had assumed the lace could be 'moulded' to a domed shape through a chemical or heat process.
Either way is better than a pleat.