We use a simple analytic model to analyze all of the published photometric observations of exoplanets. Our model has two parameters: the planets' Bond albedo, A, and its heat recirculation efficiency, epsilon. By combining the published observations for 20 exoplanets, we confirm that no single combination of albedo and recirculation efficiency fit all short-period planets. We then allow each planet to have a unique A and epsilon, and construct a two-dimensional distribution function for the albedo and recirculation efficiency of short-period planets. The only region of the A-epsilon plane that is not populated is A>0.9. The variety of recirculation efficiencies has been widely discussed, but the large range of best-fit albedos in our models is surprising. Part of the high-A distribution stems from degeneracies in the observations and from small-number statistics, but we also suggest two physical explanations. Firstly, the day-side brightness temperature of the planets exhibits a sharp rise from near-infrared to optical wavelengths. This is to be expected if either a) the optical observations are probing layers of the planet's atmosphere that are hotter than its effective temperature, which should be true by definition; and/or b) reflected light is contributing to the observed secondary eclipse depth. Secondly, some planets that have published thermal eclipse and phase variations, have energy budgets that require significant albedo.
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