The objective, design, and implementation of the OCO inverse method are presented. The inverse method is the algorithm which finds the profile-weighted mean mixing ratio, X CO2 , which best fits the measured spectrum, given a ``forward model'' which calculates the spectrum for a given atmospheric state, surface, and instrument properties. Minimizing bias among comparative values of X CO2 is a critical objective. The algorithm uses an ``optimal,'' maximum a posteriori inverse method, with weak a priori constraint, and employs a state vector containing atmospheric and surface properties expected to vary significantly between soundings. An extensive operational characterization and error analysis will be employed, producing quantities designed to aid atmospheric modelers in use of the OCO data. In particular, comparison to inverse models of surface CO2 flux will require use of the OCO column averaging kernel and a priori state vector. An off-line error analysis has also been developed for more detailed error studies, and its use is illustrated by prospective application to case studies of nadir observations in summer and winter at three sites. Uncertainties due to noise, geophysical variability, and spectroscopic parameters are considered in detail. At low and midlatitudes, the single-sounding errors due to these sources are expected to be ~0.7-0.8 ppm for high-sun conditions and ~1.5-2.5 ppm for low sun (winter). Errors from the same sources in semimonthly regional averages are predicted to be