We consider index modulation (IM) for single-carrier (SC) systems in this paper. Compared with conventional orthogonal frequency division multiplexing (OFDM) IM, the resulting approach, which is referred to as SCIM, has a better performance due to the path diversity gain under a multipath fading environment. For sparse IM, since compressive sensing (CS) algorithms can be used for low-complexity signal detection, we consider the orthogonal matching pursuit (OMP) algorithm to perform the signal detection in SCIM. A transmit diversity scheme is also proposed for both OFDM-IM and SCIM, which can not only improve the performance in terms of the diversity gain, but also increase the number of information bits per signal block.