The best known methods for combustion in Internal Combustion Engines (ICEs) are: Spark Ignition (SI), Compression Ignition (CI) and Homogeneous Charge Compression Ignition (HCCI). Each of these combustion methods has well known limitations for efficiency and clean exhaust. This paper presents a new method of combustion, called Entry Ignition (EI) that overcomes some of these limitations. EI burns a homogeneous fuel air mixture at constant pressure with combustion occurring at the inlet where the unburned mixture flows into the combustion chamber. Combustion results from the unburned mixture mixing with the much hotter burned gases already in the combustion chamber. EI can operate in a conventional piston-type engine, with the only major change being in the valving. EI’s efficiency gain results from the following. Firstly, EI is not subject to “knocking” and so can operate at CI-level compression ratios or higher. Secondly, EI allows lean burn, which improves efficiency for basic thermodynamic reasons. Thirdly, an engine using EI can fully expand the combustion gases (Brayton cycle), and finally, EI has reduced heat loss relative to the other combustion methods. These efficiency boosting effects combine independently to give a thermal efficiency of 63%, based on thermodynamic textbook-derived computer simulations. Because both EI and SI burn a homogeneous mixture, they do not produce significant particulate emissions. Also, EI can burn sufficiently lean that NOx production is kinetically suppressed, so that exhaust cleanup may be unnecessary.