  Let $p$ be a prime. We produce two new families of pro-$p$ groups which are
not realizable as absolute Galois groups of fields. To prove this we use the
1-smoothness property of absolute Galois pro-$p$ groups. Moreover, we show in
these families one has one-relator pro-$p$ groups which may not be ruled out as
absolute Galois groups employing the quadraticity of Galois cohomology (a
consequence of Rost-Voevodsky Theorem), or the vanishing of Massey products in
Galois cohomology.
