A dome for a combustion chamber may have a plurality of effusion holes therein to provide efficient cooling while preventing carbon formation on the dome and chamber walls of the combustion chamber. Conventional dome cooling designs, using dome louvers, for example, may become corroded and/or may allow for ingestion of carbon particles that may build up and eventually separate from the dome. Furthermore, the dome cooling design of the present invention allows for the use of a lower profile dome as compared with conventional domes, thereby maximizing liner volume in the constrained combustion envelope while reducing combustor case weight. Additionally, the dome effusion cooling design of the present invention requires the use of less thermal barrier coating, as compared to conventional designs, in order to minimize thermal variation within the dome and between the dome and the combustor wall. A method for uniformly cooling a dome of a combustion chamber of an engine is also disclosed.