One of the most serious challenges for speech synthesis is the systematic treatment of events in language and speech that are known to have low frequencies of occurrence. The problems that extremely unbalanced frequency distributions pose for rule-based or data-driven models are often underestimated or even unrecognized. This paper discusses the problems pertinent to rare events in four components of speech synthesis systems: in linguistic text analysis, where productive word formation processes generate a potentially unbounded lexicon and cause heavily skewed word frequency distributions; in syllabification, where some syllables occur very frequently but most phonotactically possible syllables are very infrequent; in speech timing, where most constellations of factors affecting segmental duration are sparsely or not at all represented in training databases; and in unit selection synthesis, where the uneven distribution of speech unit frequencies poses challenges to speech corpus design. Currently available techniques for coping with the problem of rare or unseen events in each of these components are reviewed. Finally, a distinction is made between a strictly closed domain with a fixed vocabulary and a merely restricted domain with loopholes for unseen words and names, and the consequences of the respective type of domain for appropriate synthesis strategies are discussed.