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Variable-length-to-block codes are a generalization of run-length codes. A coding theorem is first proved. When the codes are used to transmit information from fixed-rate sources through fixed-rate noiseless channels, buffer overflow results. The latter phenomenon is an important consideration in the retrieval of compressed data from storage. The probability of buffer overflow decreases exponentially with buffer length and we determine the relation between rate and exponent size for memoryless sources. We obtain codes that maximize the overflow exponent for any given transmission rate exceeding the source entropy and present asymptotically optimal coding algorithms whose complexity grows linearly with codeword length. It turns out that the optimum error exponents of variable-length-to-block coding are identical with those of block-to-variable-length coding and are related in an interesting way to Renyi's generalized entropy function.