Disclosed are methods and apparatus pertaining to processing in-situ, real-time data associated with fluid obtained by a downhole sampling tool. The processing includes generating a population of values for Ĉ, where each value of Ĉ is an estimated value of a fluid property for native formation fluid within the obtained fluid. The obtained data is iteratively fit to a predetermined model in linear space. The model relates the fluid property to pumpout volume or time. Each iterative fitting utilizes a different one of the values for Ĉ. A value Ĉ* is identified as the one of the values for Ĉ that minimizes model fit error in linear space based on the iterative fitting. Selected values for Ĉ that are near Ĉ* are then assessed to determine which one has a minimum integral error of nonlinearity in logarithmic space.