A sensor designed to determine the amount and concentration of analyte in a sample having a volume of less than about 1 μL. The sensor has a working electrode coated with a non-leachable redox mediator. The redox mediator acts as an electron transfer agent between the analyte and the electrode. In addition, a second electron transfer agent, such as an enzyme, can be added to facilitate the electrooxidation or electroreduction of the analyte. The redox mediator is typically a redox compound bound to a polymer. The preferred redox mediators are air-oxidizable.The amount of analyte can be determined by coulometry, amperometry, voltammetry, and potentiometry. The invention can be used to determine the concentration of a biomolecule, such as glucose or lactate, in a biological fluid, such as blood or serum. An enzyme capable of catalyzing the electrooxidation or electroreduction of the biomolecule is provided as a second electron transfer agent.