Compared with spatially-varying tone-mapping operators, global tone maps have the advantage that the input is mapped to an output image without introducing spatial artifacts common to spatially-varying tone-mapping operators (e.g. halos and intensity inversions). However some local detail can be compressed (visually lost). In this work, we propose a global tone-mapping operator that optimally, in a sum of least-squares sense, approximates spatially-varying tone-mapping operators.Our method is based on a modification of the simple but elegant constrained optimization technique called Pool-Adjacent- Violators-Algorithm (PAVA). In a second step, we show how any lost local detail can be brought back through copying, in an edge sensitive manner, detail from the original input (an approach already developed in the literature).Our new global tone-curve approach has a specific advantage: we show it suffices to learn the tone-curve by processing a small thumbnail and then produce the final output by applying the tone-curve to the full resolution input. Not only does processing on thumbnails deliver excellent results we can, using this approach, significantly increase the speed of tone-mapping operators.To evaluate our method we carried out a paired comparison psychophysical experiment. Preference scores resulting from the experiment show that in general the perceived quality of our proposed operator is similar (equally preferred) to a range of spatially-varying tone-mapping operators.