This paper discusses the challenges and methods for addressing the "zero-frequency problem" in adaptive statistical data compression. The zero-frequency problem arises when a new token is encountered in a context where it has never been seen before, requiring the encoder to assign a non-zero prediction probability despite its observed frequency being zero. The paper reviews several ad hoc approaches to this problem, including Laplace's law of succession and methods A, B, and C, and introduces a Poisson process model (P) and its close approximation (X). The Poisson model is evaluated for its ability to predict novel characters, words, and n-grams in text. The paper also compares these methods in the context of the PPM (Prediction by Partial Match) text compression technique, finding that the Poisson model and its approximation perform well, especially for words and n-grams. The modified method XC, which combines the best of both worlds, shows a slight improvement in overall coding efficiency for text files. The study concludes that the Poisson model provides uniformly better results than other methods where it applies, and that a simple approximation to it is easy to compute and accurate in practice.This paper discusses the challenges and methods for addressing the "zero-frequency problem" in adaptive statistical data compression. The zero-frequency problem arises when a new token is encountered in a context where it has never been seen before, requiring the encoder to assign a non-zero prediction probability despite its observed frequency being zero. The paper reviews several ad hoc approaches to this problem, including Laplace's law of succession and methods A, B, and C, and introduces a Poisson process model (P) and its close approximation (X). The Poisson model is evaluated for its ability to predict novel characters, words, and n-grams in text. The paper also compares these methods in the context of the PPM (Prediction by Partial Match) text compression technique, finding that the Poisson model and its approximation perform well, especially for words and n-grams. The modified method XC, which combines the best of both worlds, shows a slight improvement in overall coding efficiency for text files. The study concludes that the Poisson model provides uniformly better results than other methods where it applies, and that a simple approximation to it is easy to compute and accurate in practice.