It is common practice to bootstrap compilers of programming languages. By using the compiled language to implement the compiler, compiler developers can code in their own high-level language and gain a large-scale test case. In this paper, we investigate bootstrapping of compiler-compilers as they occur in language workbenches. Language workbenches support the development of compilers through the application of multiple collaborating domain-specific meta-languages for defining a language's syntax, analysis, code generation, and editor support. We analyze the bootstrapping problem of language workbenches in detail, propose a method for sound bootstrapping based on fixpoint compilation, and show how to conduct breaking meta-language changes in a bootstrapped language workbench. We have applied sound bootstrapping to the Spoofax language workbench and report on our experience.