Recently, several approaches have been proposed for the equalization of orthogonal frequency-division multiplexing (OFDM) signals in challenging high-mobility scenarios. Among them, a minimum mean-squared error (MMSE) block linear equalizer (BLE), based on a band LDL factorization, is particularly attractive for its good tradeoff between performance and complexity. This paper extends this approach towards two directions. First, we boost the BER performance of the BLE by designing a receiver window specially tailored to the band LDL factorization. Second, we design an MMSE block decision-feedback equalizer (BDFE) that can be modified to support receiver windowing. All the proposed banded equalizers share a similar computational complexity, which is linear in the number of subcarriers. Simulation results show that the proposed receiver architectures are effective in reducing the BER performance degradation caused by the intercarrier interference (ICI) generated by time-varying channels. We also consider a basis expansion model (BEM) channel estimation approach, to establish its impact on the BER performance of the proposed banded equalizers.