Long-term estimates of the exchange of energy (sensible heat, for example) and mass (of water and carbon) between vegetation and the atmosphere are increasing. Eddy-covariance is considered one of the most direct estimates of such exchange, and is particularly useful over ideal, flat, homogeneous sites. The proliferation of continuous and long term eddy-covariance studies (e.g. the AmeriFlux program) for the assessment of ecosystem carbon and water budgets is forcing us to apply these methods under conditions and locations that have been eschewed in the past. How to interpret eddy-covariance measurements under non-ideal conditions needs to be re-assessed, starting from first principles, i.e., the conservation equation. Equations are developed and applied to assess the accuracy of eddy-flux estimates of exchange for non-ideal sites and under non-ideal conditions, such as tall forests and typical diurnal cycling. Significant corrections are shown to be necessary under some conditions and for some sites.