Whether the goal is to fill gaps in the flux record, or to extract physiological parameters from eddy covariance data, researchers are frequently interested in fitting simple models of ecosystem physiology to measured data. Presently, there is no consensus on the best models to use, or the ideal optimization criteria. We demonstrate that, given our estimates of the distribution of the stochastic uncertainty in nighttime flux measurements at the Howland (Maine, USA) AmeriFlux site, it is incorrect to fit ecosystem respiration models using ordinary least squares (OLS) optimization. Results indicate that the flux uncertainty follows a double-exponential (Laplace) distribution, and the standard deviation of the uncertainty (σ(δ )) follows a strong seasonal pattern, increasing as an exponential function of temperature. These characteristics both violate OLS assumptions. We propose that to obtain maximum likelihood estimates of model parameters, fitting should be based on minimizing the weighted sum of the absolute deviations: ∑|measured−modeled|/σ(δ). We examine in detail the effects of this fitting paradigm on the parameter estimates and model predictions for three simple but commonly used models of ecosystem respiration. The exponential Lloyd & Taylor model consistently provides the best fit to the measured data. Using the absolute deviation criterion reduces the estimated annual sum of respiration by about 10% (70–145 g C m−2 y−1) compared to OLS; this is comparable in magnitude but opposite in sign to the effect of filtering nighttime data using a range of plausible u* thresholds. The weighting scheme also influences the annual sum of respiration: specifying σ(δ) as a function of air temperature consistently results in the smallest totals. However, annual sums are, in most cases, comparable (within uncertainty estimates) regardless of the model used. Monte Carlo simulations indicate that a 95% confidence interval for the annual sum of respiration is about ±20–40 g C m−2 y−1, but varies somewhat depending on model, optimization criterion, and, most importantly, weighting scheme.