We describe and demonstrate a multiloop technique for single-mode selection in an optoelectronic oscillator (OEO). We present experimental results of a dual loop OEO, free running at 10 GHz, that has the lowest phase noise (-140 dBc/Hz at 10 kHz from carrier) of all free-running room-temperature oscillators to date. Finally, we demonstrate the first fiber-optic implementation of the carrier suppression technique to further reduce the close-to-carrier phase noise of the oscillator by at least 20 dB.