Time-domain channel shortening filters (CSFs) are used in orthogonal frequency division multiplexing (OFDM) systems to increase the spectral efficiency. We consider transmit-side CSF to reduce the cyclic prefix (CP) length required for the OFDM symbol. We first construct a simple CSF scheme which, however, has a poorer spectral efficiency (SE) when compared to a system with adequate CP length (which we refer to as a full-CP system). We then propose a modified CSF (MCSF) structure that exploits the null-space of an under-determined system of equations, and provides independent equivalent channels to the receiver. The SE of the MCSF is shown to be generally higher than the full-CP system when the chosen CP length is significantly smaller than the channel delay spread. Simulated BLER performance for turbo-coded multi-antenna OFDM systems reveals that the MCSF can provide up to 2 dB gain in <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">${{\bf E}_{\bf b}}/{{\bf N}_{\bf 0}}$</tex></formula> when compared with the full-CP system for the same transmit information rate.