Index modulation concept has attracted considerable research interest in the past few years. As a realization of index modulation in the frequency domain, orthogonal frequency division multiplexing with index modulation (OFDM-IM) has recently been proposed, which conveys information bits through both the subcarrier activation patterns and the amplitude phase modulation constellation points. This paper proposes two enhanced OFDM-IM schemes aimed at achieving higher spectral efficiency and diversity gain, respectively. The first one, termed OFDM with hybrid in-phase/quadrature index modulation (OFDM-HIQ-IM), explores the I-and Q-dimensions jointly for index modulation, allowing transmission of more index modulation bits in each subcarrier group. The second one, termed linear constellation precoded OFDM-IQ-IM (LP-OFDM-IQ-IM), spreads information symbols across two adjacent active subcarriers through linear constellation precoding to harvest additional diversity gain. By maximizing the minimum squared Euclidean distance, two different realizations of LP-OFDM-IQ-IM are derived, which leads to a rotated and a diamond shaped constellation, respectively. The proposed OFDM-HIQ-IM and LP-OFDM-IQ-IM, as revealed by both theoretical analyses and computer simulations, enable low-complexity detection and exhibit superior error rate performance over the existing OFDM-IM schemes.