In this paper, we investigate cooperative diversity as a fading mitigation technique for Free-Space Optical (FSO) communications with intensity modulation and direct detection (IM/DD). In particular, we propose two novel one-relay cooperation strategies. The first scheme does not require any feedback and is based on selective relaying where the relay forwards only the symbols that it detected with a certain level of certainty that we quantify in both cases of absence or presence of background radiation. This technique results in additional performance enhancements and energy savings compared to the existing FSO cooperative techniques. The second scheme can be applied in situations where a feedback link is available. This scheme that requires only one bit of feedback results in significant performance gains over the entire range of the received signal level.