Orthogonal frequency division multiplexing (OFDM) has proven itself as an effective multicarrier digital communication technique. In recent years, the interest in optical OFDM has grown significantly, due to its spectral efficiency and inherent resilience to frequency-selective channels and to narrowband interference. For these reasons, it is currently considered to be one of the leading candidates for deployment in short fiber links such as the ones intended for inter-data-center communications. In this paper, we present a new power-efficient symbol recovery scheme for dc-biased optical OFDM (DCO-OFDM) in an intensity-modulation direct-detection (IM/DD) system. We introduce an alternative method for clipping in order to maintain a nonnegative real-valued signal and still preserve information, which is lost when using clipping, and propose an iterative detection algorithm for this method. A reduction of $\text{50\%}$ in the transmitted optical power along with an increase of signal-independent noise immunity (gaining 3 dB in SNR), compared to traditional DCO-OFDM with a dc bias of standard deviations of the OFDM signal, is attained by our new scheme for a symbol error rate of in a QPSK constellation additive white Gaussian noise flat channel model.