A speech recognition system comprises exactly two automated speech recognition (ASR) engines connected to receive the same inputs. Each engine produces a recognition output, a hypothesis. The system implements one of two (or both) methods for combining the output of the two engines. In one method, a confusion matrix statistically generated for each speech recognition engine is converted into an alternatives matrix in which every column is ordered by highest-to-lowest probability. A program loop is set up in which the recognition outputs of the speech recognition engines are cross-compared with the alternatives matrices. If the output from the first ASR engine matches an alternative, its output is adopted as the final output. If the vectors provided by the alternatives matrices are exhausted without finding a match, the output from the first speech recognition engine is adopted as the final output. In a second method, the confusion matrix for each ASR engine is converted into Bayesian probability matrix.