Provided herein are systems and methods for operating carbon oxide (COx) reduction reactors (CRRs) for producing methane (CH4). Embodiments of the systems and methods may also be used for producing other organic compounds including alcohols, carboxylic acids, and other hydrocarbons such as ethylene (CH2CH2). According to various embodiments, the systems and methods may be characterized by one or more of the following features. In some embodiments, a membrane electrode assembly (MEA) includes a cathode catalyst layer with a relatively low catalyst loading. In some embodiments, a bipolar MEA includes a thin cation-conducting layer and a thin anion-conducting layer, with the cation-conducting layer being thicker than the anion-conducting layer. In other embodiments a pure anion exchange polymer only membrane may be used to bridge the cathode catalyst and the anode catalyst. These and other features are described further below.