In this paper, we propose computationally efficient and high-quality methods for statistical voice conversion (VC) with direct waveform modification based on spectral differentials. The conventional method with a minimum-phase filter achieves high-quality conversion but requires heavy computation in filtering. This is because the minimum phase using a fixed lifter of the Hilbert transform often results in a long-tap filter. One of our methods is a data-driven method for lifter training. Since this method takes filter truncation into account in training, it can shorten the tap length of the filter while preserving conversion accuracy. Our other method is sub-band processing for extending the conventional method from narrow-band (16 kHz) to full-band (48 kHz) VC, which can convert a full-band waveform with higher converted-speech quality. Experimental results indicate that 1) the proposed lifter-training method for narrow-band VC can shorten the tap length to 1/16 without degrading the converted-speech quality and 2) the proposed sub-band-processing method for full-band VC can improve the converted-speech quality than the conventional method.