A low-headroom current driver does not use an op amp or resistor. A sensing transistor having its source connected to a drain of an output transistor senses variations in an output current. The gate, source, and drain voltages of the sensing transistor are mirrored to a sense mirror transistor to control a sense current. The sense current is mirrored to a reference source transistor to generate a mirrored sense current. An error between the mirrored sense current and a fixed reference current is stored as charge on an error-storing capacitor. The stored error charge creates a negative-feedback compensation current that adjusts a gate voltage generated by a feedback-driving transistor. The adjusted gate voltage controls the gate of the output transistor to compensate for the sensed variation in output current. The sensing current is also compensated using a sense-mirror tail transistor connected to the sense mirror transistor.