The three classic Futamura projections stand as a cornerstone in the development of partial evaluation. The observation by Futamura [1983], that compiler generators produced by his third projection are self-generating, and the insight by Klimov and Romanenko [1987], that Futamura's abstraction scheme can be continued beyond the three projections, are systematically investigated, and several new applications for compiler generators are proposed. Possible applications include the generation of quasi-online compiler generators and of compiler generators for domain-specific languages, and the bootstrapping of compiler generators from program specializers. From a theoretical viewpoint, there is equality between the class of self-generating compiler generators and the class of compiler generators produced by the third Futamura projection. This exposition may lead to new practical applications of compiler generators, as well as deepen our theoretical understanding of program specialization.