The limited bandwidth of optical wireless communication (OWC) front-end devices motivates the use of multiple-input-multiple-output (MIMO) techniques to enhance data rates. It is known that very high multiplexing gains could be achieved by spatial multiplexing (SMX) in exchange for exhaustive detection complexity. Alternatively, in spatial modulation (SM), a single light emitting diode (LED) is activated per time instance where information is carried by both the signal and the LED index. Since only an LED is active, both transmitter (TX) and receiver (RX) complexity reduces significantly while retaining the information transmission in the spatial domain. However, significant spectral efficiency losses occur in SM compared to SMX. In this paper, we propose a technique which adopts the advantages of both systems. Accordingly, the proposed flexible LED index modulation (FLIM) technique harnesses the inactive state of the LEDs as a transmit symbol. Therefore, the number of active LEDs changes in each transmission, unlike conventional techniques. Moreover, the system complexity is reduced by employing a linear minimum mean squared error (MMSE) equalizer and an angle perturbed receiver at the RX. Numerical results show that FLIM outperforms the reference systems by at least 6 dB in the low and medium/high spectral efficiency regions.