  We show that a strong vanishing conjecture for $n$-fold Massey products holds
for fields of virtual cohomological dimension at most $1$ using a theorem of
Haran. We also prove the same for PpC fields, using results of Haran--Jarden.
Finally we construct a pro-$2$ group which satisfies the weak Massey vanishing
property for every $n\geq3$, but does not satisfy the strong Massey vanishing
property for $n=4$.
