The estimation of motion direction from time varying retinal images is a fundamental task of visual systems. Neurons that selectively respond to directional visual motion are found in almost all species. In many of them already in the retina direction selective neurons signal their preferred direction of movement. Scientific evidences suggest that direction selectivity is carried from the retina to higher brain areas. Here we adopt a simple integrate-and-fire neuron model, inspired by recent work of Casti et al. (2008), to investigate how directional selectivity changes in cells postsynaptic to directional selective retinal ganglion cells (DSRGC). Our model analysis shows that directional selectivity in the postsynaptic cells increases over a wide parameter range. The degree of directional selectivity positively correlates with the probability of burst-like firing of presynaptic DSRGCs. Postsynaptic potentials summation and spike threshold act together as a temporal filter upon the input spike train. Prior to the intricacy of neural circuitry between retina and higher brain areas, we suggest that sharpening is a straightforward result of the intrinsic spiking pattern of the DSRGCs combined with the summation of excitatory postsynaptic potentials and the spike threshold in postsynaptic neurons.