This article analyzes trends in prison rates and mental hospital rates in France since the earliest available statistics. It shows that, on almost two centuries of data and amidst an agitated political history, every asylum trend in France is "countered" by an inverse prison trend, and vice-versa. Both trends are like a mirror image of each other. We reflect on the possible explanations for this intriguing fact and show that the most obvious ones (a population transfer or a building transfer) are not able to account for most of the relationship. After these explanations have been dismissed, we are left with an enigma with wide theoretical and practical implications. How is it that when prisons fall, asylums rise and when prison rise, asylums fall? We suggest possible research avenues drawing on the 1960s and 1970s critical literature on "total institutions" and offer implications for current theories of the "punitive turn" and current quantitative studies of prison rates.