Technical Abstract: The model of Farquhar, von Caemmerer and Berry has long been the standard in relating photosynthetic carbon assimilation and intercellular CO2 concentration. Assimilation is segmented into three regions, each modeled by a distinct function. Disjunct fitting of the component functions is customarily used, requiring preliminary subsetting of data into sets believed to correspond to each region. Where to subset is at the discretion of the investigator, and each parameter is estimated using less than all available information. Added operations also make analyzing large amounts of gas exchange data unduly laborious. We show how multiple segments can be estimated simultaneously, using the entire dataset at once, without predetermination of transitions. The method is shown to be fast, and to lend itself to rapid recursive processing. Investigation of the number of estimable parameters suggests that three parameters at least have excellent statistical properties, but that estimating more than three may be difficult. Illustrations of software programming are provided, and a review of difficulties and their solutions.