1. In a machine translation system or a speech recognition system, a method performed on at least one processor, comprising, processing an output candidate comprising a sequence of tokens for natural language input, including estimating an estimated probability for a token in the sequence of tokens based upon actual counts corresponding to a number of zero or more times that the sequence was observed in training data, including controlling interpolation parameters independently from controlling a discount parameter, and when the sequence was observed at least once, computing a discount probability based upon the discount parameter subtracted from a maximum likelihood probability estimate that is based upon a context corresponding to the sequence, computing an interpolation probability based upon one interpolation parameter and a smaller other context corresponding to the sequence, mathematically combining the discount probability with the interpolation probability to provide the estimated probability, and using the estimated probability to generate an alternative output for at least a portion of the natural language input.