Babies weighing under 6 kg are difficult to dialyse, especially those as small as 1 kg. Peritoneal dialysis is easier than haemodialysis, but is not always possible, and clears molecules less efficiently. Two factors complicate haemodialysis. First, extracorporeal circuits are large relative to a baby's blood volume, necessitating priming with fresh or modified blood. Second, blood flow from infants' access vessels is disproportionately low (Poiseuille's law), causing inadequate dialysis, or clotting within the circuit. These problems are minimised by using single lumen access, a very small circuit, and a reservoir syringe to separate the sampling and dialyser blood flow rates. Its manual operation is tedious, so we developed a computer-controlled, pressure-monitored machine to run it, including adjusting the blood withdrawal rate from poorly sampling lines. We have dialysed four babies weighing 0.8-3.4 kg, with renal failure or metabolic disorders. The circuits did not require priming. Clearances of creatinine, urea, potassium, phosphate and ammonia were mean (SD) 0.54 (0.22) ml/min using one dialyser, and 0.98 (0.22) ml/min using two in parallel. Ammonia clearance in a 2.4 kg baby had a 9 h half-life. Ultrafiltration up to 45 ml/h was achieved easily. This device provided infants with immediate, effective and convenient haemodialysis, typically delivered for prolonged periods.