In this paper, a novel multicarrier modulation scheme called Filtered Orthogonal Frequency Division Multiplexing with Index Modulation has been proposed for operation over frequency-selective and rapidly time-varying wireless fading channels. The filtering helps restricting the Out-of-Band Emission and indexing helps in reducing Transmitter Power. The performance of the proposed modulation scheme is compared with traditional multicarrier and index modulated multicarrier schemes to show that the proposed method is much better in terms of Out-of-Band power leakage. Indexing apparently reduces transmit data rate of the system. This paper also shows how to circumvent this apparent reduction in spectral efficiency without degrading other system parameters.