Incremental relaying is a spectral-efficient relaying approach which introduces itself as one of the possible solutions to the spectrum scarcity problem for future generations of cellular communications systems. In this paper, we study threshold amplify-and-forward incremental relaying for correlated fading channels, i.e., fading channels for which the channel gain amplitude varies during the time interval of a block transmission; however, the variation occurs in a correlating fashion. From this aspect, these channels are different from both block-fading and fast-fading channels. Due to the correlating nature of the channels, it is possible to compress channel state information (CSI) sequences and employ the compressed CSI sequences as side information to carefully select the bits transmitted by the relay. This idea is already employed in previous works to increase the spectral efficiency; however, those works consider block-fading channels and also assume maximal ratio combining (MRC) at receiver. In case of MRC, explicit expressions for the end-to-end signal-to-noise ratio (SNR) exist, which enable packet error rate analysis by aid of Moment Generating Functions of the SNR. However, to apply MRC, the receiver requires all channel gains (including source-relay channel gain). In case of correlated channels, communicating all real-valued channel gains, requires a large overhead. This fact renders applicability of MRC for correlated channels. We apply the more practical Equal-Gain Combining method. We derive series approximations for symbol error rate, given M-QAM and MPSK modulations, and assuming Nakagami-m fading channels. We also analyze the spectral efficiency by assuming Markov models for the channels. We compare the spectral efficiency in case of correlated and fast-fading channels and show that, unlike fast-fading channels, correlated fading channels allow for a spectrally efficient scheme.