A method of duplex printing on a cut sheet printer having a sheet supply system for feeding sheets to a print station in a first orientation for printing a first image on the first side of the sheet and then in a second orientation for printing a second image on a second side of the sheet includes, for each sheet: (a) estimating a likelihood P1 that, in a print process for printing the first image, the sheet will become damaged to such an extent that the damage will compromise a later print process for printing the second image; (b) comparing the likelihood P1 to a threshold T; and (c) if the likelihood P1 exceeds the threshold T, reversing the print order so that the second image is printed before the first image. The method ensures that the riskier image is printed on the duplex pass. The chances of the sheet with the simplex image then successfully passing through the duplex pass are then increased.