The fabrication of microdevices for fluidic control often requires the use of flexible diaphragms in a way that requires cleanroom equipment and compromises performance. We use a CO2 laser to perform the standard ablative techniques of cutting and engraving materials, but we also apply a method that we call laser placement. This allows us to fabricate precisely-positioned and precisely-sized, isolated diaphragms. This in turn enables the rapid prototyping of integrated multilayer microfluidic devices to form complex structures without the need for manual positioning or cleanroom equipment. The fabrication process is also remarkably rapid and capable of being scaled to manufacturing levels of production. We explore the use of these devices to construct a compact system of peristaltic pumps that can form water in oil droplets without the use of the non-pulsatile pumping systems typically required. Many devices can be fabricated at a time on a sheet by sheet basis with a fabrication process that, to our knowledge, is the fastest reported to date for devices of this type (requiring only 3 h). Moreover, this system is unusually compact and self-contained.