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In this work, system adaptation under measurement uncertainty is considered for environments where there exist accurate statistical models of how the desired parameter depends on the available measurements. First, previous work on robust adaptive coded modulation using outdated multipath fading estimates is reviewed. The same ideology is then applied to power control when there is statistical uncertainty in the measurement of the path loss and log-normal shadowing. For a single-user system, a closed form power control rule is found, and numerical results are presented which suggest a moderate gain over systems which employ traditional power control functions with an energy margin to compensate for measurement uncertainty. The analogous multi-user power control problem is straightforward to pose, but it has not been amenable to closed form solution to this point.