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This paper presents a new control strategy for Power Factor Correctors (PFCs) used to drive High-Brightness Light-Emitting Diodes (HB-LEDs). This control strategy is extremely simple and is based on the use of a standard Peak Current-Mode Integrated Controllers (PCMIC) reducing its cost and complexity in comparison to traditional PFC controllers. In fact, this method is an alternative implementation of the One Cycle Control (OCC) to PFCs belonging to the Flyback family of converters, without introducing high complexity for reducing the Total Harmonic Distortion (THD). In this case, the use of a simple exponential compensation ramp instead of a linear one is the proposed solution for drawing a sinusoidal input current. Moreover, the line current is cycle-by-cycle controlled and, therefore, the input current feedback loop is extremely fast, which allows the use of this type of control with high frequency lines. The proposed idea is to apply this simple control to a single stage PFC in order to design a low-cost AC-DC HB-LED driver. Finally, an experimental prototype of this driver was developed.