  Using the block filtration as a realisation of the coradical filtration, we
study the discrepancy between the depth filtration and the coradical filtration
for motivic multiple zeta values. We construct an explicit dictionary between a
certain subspace of block graded multiple zeta values and totally odd multiple
zeta values and show that all expected relations in the depth graded motivic
Lie algebra may be realised in the block graded Lie algebra as the kernel of an
explicit map. We also discuss some connections to the uneven Broadhurst-Kreimer
conjecture, and outline a possible approach.
