The class of good semigroups is a class of subsemigroups of $${\mathbb {N}}^h$$ N h , that includes the value semigroups of rings associated to curve singularities and their blowups, and allows to study combinatorically the properties of these rings. In this paper we give a characterization of almost symmetric good subsemigroups of $${\mathbb {N}}^h$$ N h , extending known results in numerical semigroup theory and in one-dimensional ring theory, and we apply these results to obtain new results on almost Gorenstein one-dimensional analytically unramified rings.