Hypernatremia usually results from the loss of water from the body in excess of loss of electrolytes. Although urinary loss of free water is usually thought of when the urine is dilute, it can also occur when the urine is relatively concentrated, for example after administration of osmotic diuretics. We present a case of hypernatremia in the setting of resolving acute renal failure. Quantitative analysis of urinary losses and the concept of electrolyte-free water clearance help to explain the development and persistence of hypernatremia in this case. Urine in such cases is typically rich in urea (an irrelevant osmole from the perspective of plasma sodium) with low concentrations of sodium and potassium (osmoles that determine plasma sodium concentration). So from the perspective of plasma sodium-determining osmoles (sodium and potassium) this hyperosmolar urine is actually "dilute", resulting in loss of free water and a rise in the plasma sodium concentration. This case illustrates the utility of the electrolyte-free water concept in understanding the development of hypernatremia in resolving acute renal failure. We discuss the evolution of these concepts and how they can be applied to typical clinical situations.