The widespread application of OFDM for local area mobile wireless broadband systems is strongly motivated by the simple equalization it affords. OFDM's bottleneck of channel-dependent performance was only previously addressed by replacing the cyclic prefix (CP) with trailing zeros (TZ). Such zero-padded OFDM transmissions enable FIR channel-irrespective symbol recovery which results in significant BER gains. The price paid is increased receiver complexity compared to the classical CP-OFDM. To reduce complexity, this paper proposes two novel equalizers for TZ-OFDM. One is based on an overlap and add approach and exhibits exactly the same performance and complexity as CP-OFDM. The second offers BER performance close to the TZ-OFDM MMSE equalizer and incurs a moderate complexity increase. An extension of an existing CP-OFDM pilot-based channel estimation method is also derived for the proposed equalization schemes. Simulations are conducted in a realistic HiperLAN/2 scenario comparing the various OFDM transceivers.