A catalyst regenerator (100) has a first section (110) and a second section (120) and is operated such that carbon from a carbon-contaminated catalyst (140) is converted to carbon monoxide in the first section (110) and that carbon monoxide is converted to carbon dioxide in the second section (120). The residence time of the oxygen-containing gas in the first and second sections (110, 120) is regulated in preferred configurations by the shape (e.g., diameter) of the first and second sections (110, 120).