Haemodialysing small infants is difficult because of vascular access limitations. We show that Poiseuille's law (that flow through a tube varies with its radius4) makes it inevitable that the blood flow that can be achieved in smaller patients will fall disproportionately compared to their need for dialysis. Poiseuille's law also predicts that for single and multiple lumen cannulae of the same outside gauge, blood flow through the single lumen will be several times greater. Measurements confirmed this. It is argued that haemodialysis efficiency will therefore be improved by using a single lumen cannula to alternately withdraw and return blood, compared to sampling and returning continuously through a multiple lumen cannula, despite only withdrawing for half the time.