In this paper we analyze a turbo equalization scheme that combines maximum a posteriori probability (MAP) equalization and turbo decoding. Our aim is to optimize the turbo equalizer in order to approach the information capacity limit for channels with severe inter-symbol interference (ISI). For this purpose, we perform an extensive search for turbo codes that give an SNR-BER performance closest to the channel information capacity limit. Our results show that the optimized turbo equalizer can approach the information capacity limit to within 0.7 dB. We also optimize the turbo equalizer in terms of the minimum number of required turbo decoding iterations. Our results show that a turbo decoder within a turbo equalization loop requires only a small number of iterations. Finally, our analysis reveals that when there are turbo codes with similar extrinsic information transfer characteristics, the computational complexity can be reduced by choosing the code with the smallest constraint length with no loss in SNR-BER performance.