Optical wireless (OW) technology is attractive for short-range high-speed transmission, especially in RF sensitive environments or where secure applications are desired. We consider transmission over a broadband OW channel, present in the non-directed line-of-sight (LOS) link. For communication, we assume a system concept based on a modulation-adaptive OFDM (DMT). Such system offers efficient channel capacity exploitation, while avoiding inconvenient pointing and tracking mechanisms. Moreover, it allows deployment of simple optical components and efficient electrical signal processing. We first show that the dynamically adaptive system can provide great transmission rate enhancements compared to the statically designed one, even assuming a very conservative constraint on the electrical signal waveform (i.e., no clipping). Then, we show that significant further improvements can be achieved by tolerating some clipping, at the cost of accepting a minor increase of the symbol error rate.