Thanks, very useful information.
8 coefficients sounds very realistic. I got optimal results more or less
regularly for a 16-tap FIR, but I think that's where it ends.
An alternative I'll try - not because of real need but curiosity - is some
Round-Robin scheme for iterative reweighted least-squares in a cascade of
filters. The idea is that for small weight changes, each filter should
'attract' the weight at frequencies where the LS solver can improve more
easily than the other stages.
But, whether this works, remains to be seen.