In orthogonal frequency division multiplexing with index modulation (OFDM-IM), the active subcarriers can convey information bits by modulated symbols as well as their indices. OFDM-IM has attracted a great deal of attention from researchers by virtue of high energy efficiency. Unfortunately, OFDM-IM has inherited large peak-to-average power ratio (PAPR) of the classical OFDM signal, but there are few works dealing with it. Selected mapping (SLM) is a promising PAPR reduction technique that is distortionless, has good PAPR reducing capability, and can be easily adapted in OFDM-IM systems. In SLM for OFDM-IM systems, the phase sequences rotate the OFDM-IM block in the frequency domain before the inverse fast Fourier transform (IFFT) is applied. Also, permutation in the frequency domain can be easily introduced before multiplication of phase sequences in SLM. In this paper, we investigate the phase sequence set (PSS) and permutation functions in the SLM scheme for OFDM-IM systems; First, the efficiency of the permutation is analyzed as a function of the number of active subcarriers. Second, the optimal conditions for the PSS and permutation functions are derived, which is verified through simulations.