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Let p be a prime. A pro-p group G is said to be 1-smooth if it can be endowed with a continuous representation 
$\theta \colon G\to \mathrm {GL}_1(\mathbb {Z}_p)$
such that every open subgroup H of G, together with the restriction 
$\theta \vert _H$
, satisfies a formal version of Hilbert 90. We prove that every 1-smooth pro-p group contains a unique maximal closed abelian normal subgroup, in analogy with a result by Engler and Koenigsmann on maximal pro-p Galois groups of fields, and that if a 1-smooth pro-p group is solvable, then it is locally uniformly powerful, in analogy with a result by Ware on maximal pro-p Galois groups of fields. Finally, we ask whether 1-smooth pro-p groups satisfy a “Tits’ alternative.”
