We study characteristics of the second significant digits of block-DCT coefficients computed from digital images. Following previous works on compression forensics based on first significant digits, we examine the merits of stepping towards significant digits beyond the first. Our empirical findings indicate that certain block-DCT modes follow Benford's law of second significant digits extremely well, which allows us to distinguish between never-compressed images and decompressed JPEG images even for the highest JPEG compression quality of 100. As for multiple-compression forensics we report that second significant digit histograms are highly informative on their own, yet cannot further improve already good performances of classification schemes that work with first significant digits alone.