Adaptive spatial modulation (ASM), where the modulation orders assigned to transmit antennas are dynamically adapted to the changing channel conditions, is a new limited-feedback multiple-input-multiple-output (MIMO) transmission technique. However, the exhaustive search for the optimal modulation order vector in ASM requires very high computational complexity and feedback load. In this paper, we propose two simplified ASM (SASM) schemes that reduce the high computational complexity and feedback load with negligible performance loss. More specifically, a candidate-reduction-based ASM (CR-ASM) that exploits the candidate selection probability is first developed to shrink the search space. The CR-ASM scheme only considers the candidates with high probability. To further reduce the complexity, another SASM scheme that uses a one-bit reallocation (OBRA) algorithm for modulation order assignment is proposed. Regardless of the number of transmit antennas, OBRA only needs to consider the transmit antenna pair with the highest correlation and selects their optimum orders among four possible candidates, which significantly reduce the search complexity. Simulation results show that the proposed schemes substantially reduce computational cost and feedback load while maintaining the benefits of the conventional ASM, particularly for a high number of transmit antennas.