—We present the ǫ-outage capacity in the low signal-to-noise ratio (SNR) regime of an incremental relaying network. The network consists of one source, one destination, and two half-duplex relays. The one-bit feedback from the destination node is considered to be imperfect and is modeled as binary symmetric channel. The basic idea is that in each block only one terminal transmits depending on the feedback information in order to achieve a better use of the degrees of freedom of the channel. We derive a closed-form expression of the ǫ-outage capacity and show that the quality of the feedback link has a great influence on the ǫ-outage capacity of the network. We further examine an extension to the “usual” incremental relaying protocol by allowing the relays to overhear the transmissions of each other in order to increase their own decoding probability. This novel incremental relaying protocol performs close to the cut-set bound (within 0.5 bit/s/Hz). Keywords— cooperative com...