In this paper, an optimized fractional order conditional integrator (OFOCI) is proposed. The key feature of this OFOCI is that, the fractional order of the integrator and the output parameter for the "hold" value in the course of conditional integration, can be tuned following the analytical optimality design specifications, to achieve the optimized performance not achievable for integer order conditional integrators (IOCIs). The proposed optimality specifications are given to satisfy the desired phase delay of the conditional integrator, and to minimize the concerned high order harmonic magnitude ratio. The numerical solution of calculating the optimized parameters of the OFOCI is introduced. The phase delays and the magnitude ratios of four OFOCIs designed according to four different phase delays are compared with the IOCIs. Simulation results with the FFT spectra are also presented to illustrate the theoretical analysis. (C) 2011 Elsevier Ltd. All rights reserved.