Pumped thermal energy storage (PTES) and liquid air energy storage (LAES) are two large-scale electricity storage technologies that store energy in the form of thermal exergy. This is achieved by operating mechanically-driven thermodynamic cycles between thermally insulated storage tanks. Both technologies are free from geographic restrictions that apply to pumped hydro and most compressed air storage. The present paper describes a novel, combined system in which PTES operates as a topping cycle and LAES as a bottoming cycle. The fundamental advantage is that the cold thermal reservoirs that would be required by the two separate cycles are replaced by a single heat exchanger that acts between them, thereby saving significant amounts of storage media per unit of energy stored. In order to reach cryogenic temperatures, the PTES cycle employs helium as the working fluid, while the LAES cycle uses supercritical air (at around 150 bar) which is cooled sufficiently to be fully liquefied upon expansion, thus avoiding recirculation of leftover vapour. A thermodynamic study of a baseline configuration of the combined cycle is presented and results are compared with those of the separate systems. These indicate that the new cycle has a similar round-trip efficiency to that of the separate systems while providing a significantly larger energy density. Furthermore, three adaptations of the base-case combined cycle are proposed and optimised. The best of these adaptations achieves an increase in thermodynamic efficiency of about 10 percent points (from 60 % to 70 %), therefore significantly exceeding the individual cycles in both energy density and efficiency.