We have investigated statistical list-mode reconstruction applicable to a depth-encoding high resolution research tomograph. An image non-negativity constraint has been employed in the reconstructions and is shown to effectively remove the overestimation bias introduced by the sinogram non-negativity constraint. We have furthermore implemented a convergent subsetized (CS) list-mode reconstruction algorithm, based on previous work (Hsiao et al 2002 Conf. Rec. SPIE Med. Imaging 4684 10-19; Hsiao et al 2002 Conf. Rec. IEEE Int. Symp. Biomed. Imaging 409-12) on convergent histogram OSEM reconstruction. We have demonstrated that the first step of the convergent algorithm is exactly equivalent (unlike the histogram-mode case) to the regular subsetized list-mode EM algorithm, while the second and final step takes the form of additive updates in image space. We have shown that in terms of contrast, noise as well as FWHM width behaviour, the CS algorithm is robust and does not result in limit cycles. A hybrid algorithm based on the ordinary and the convergent algorithms is also proposed, and is shown to combine the advantages of the two algorithms (i.e. it is able to reach a higher image quality in fewer iterations while maintaining the convergent behaviour), making the hybrid approach a good alternative to the ordinary subsetized list-mode EM algorithm.