It's said that for FIR filters, you can select control of phase, frequency response or latency, but not all simultaneously. Typically, SINC kernels are arranged with the best possible frequency response and linear phase characteristics. However, it's possible to give up on the linear phase property to reduce latency.
Normally SINC is a symmetric filter with mirrored halves around its midpoint, and the large values of the kernel occur at the midpoint. Therefore, at 256 taps it causes a delay of about 128 samples, with about 128 samples of ringing around the midpoint of the action of the filter kernel.
A minimum-phase reconstruction of the same filter can probably reduce the latency to just a few dozen taps, because the large values of the sinc kernel are arranged to happen as early as possible in the filter. The ringing, then, takes the rest of the kernel and has somewhat larger amplitude.
I don't think the human ear is sensitive to phase at all, especially at the highest frequencies, so I'd love if more people at least considered minimum phase filters.