Isobaric expansion (IE) technology is a promising solution for mini- and medium-scale low-grade heat utilization. IE engines directly convert heat to mechanical energy and are particularly interesting as direct-acting, vapor-driven pumps and compressors. The elimination of multiple energy transformations, technical simplicity and the ability to use widely available low-grade heat (<100 °C) instead of fossil fuels are attractive features of this technology. The purpose of this paper was to present a new compression technology based on IE Worthington type engines, analyze the process analytically and numerically, and provide a first assessment of its potential. The simplest single- and double-acting schemes were considered for arbitrary low and high pressures of the compressed gas/vapor and driving vapor. In these schemes, the compressor piston was rigidly connected to that of an engine/driver. The vapor use efficiency of the driver process was characterized by the ratio of the network carried out in the cycle to the consumed mass of the driving vapor. The performed thermodynamic analysis showed how the vapor use efficiency depends on the process parameters. It was found that the efficiency of vapor use in the simplest schemes was low in comparison with the efficiency in pumps if the compressor work was much less than the pump work at the same pressure ratio. This occurred because the energy of the driving vapor was spent on the compression of the vapor itself. As a result, the thermal efficiency of the IE engine compressors was lower than that of the IE engine pumps. The difference was very large if the work of the engine feed pump was significant and no heat regeneration is applied. The results obtained are very useful for achieving improvements in this interesting technology, which will be reported in subsequent publications.