We routinely encounter digital color images that were previously JPEG-compressed. We aim to retrieve the various settings - termed JPEG compression history (CH) - employed during previous JPEG operations. This information is often discarded en-route to the image's current representation. The discrete cosine transform coefficient histograms of previously JPEG-compressed images exhibit near-periodic behavior due to quantization. We propose a statistical approach to exploit this structure and thereby estimate the image's CH. Using simulations, we first demonstrate the accuracy of our estimation. Further, we show that JPEG recompression performed by exploiting the estimated CH strikes an excellent file-size versus distortion tradeoff.