How far can we push cost-effective energy efficiency if power costs 10 times today's utility price and is extremely scarce? Many situations today operate under these conditions, generally in buildings or vehicles that generate their own power, such as military forward bases, disaster response centers, remote, off-grid sites, and hospitals or other critical facilities operating on backup power. This paper examines these applications as a unified "market," where 80-90% energy efficiency improvements are not only cost-effective but can help these facilities better carry out their mission. Clear advantages of high efficiency include longer operation between fuel and battery resupply, longer vehicle ranges, and ultimately the ability to operate autonomously using locally available renewable energy sources. We first summarize the energy use characteristics and operational needs of several applications that would benefit from such extreme efficiency. We then identify ultra-efficient design options for a wide variety of equipment used in such facilities, including lighting, space conditioning, water heating, cooking and cleaning appliances, electronics, pumps and motors. Savings of 50-90% are possible using technologies that are either commercially available or close to production, and further savings are possible using advanced technologies that are still in development. Several cross-cutting strategies apply to a wide range of equipment, including electronic lighting, heat pump technology, power management, variable-speed drives, sensors and controls, and high-efficiency motors. By designing products to meet the efficiency needs of extreme applications, this market niche can be used as a market transformation strategy to bring these advanced technologies into broader commercial production much sooner than traditional building applications.