Pseudocompact totally dense subgroups

It was shown by Dikranjan and Shakhmatov in 1992 that if a compact abelian group admits a proper totally dense pseudocompact subgroup, then cannot have a torsion closed -subgroup; moreover this condition was shown to be also sufficient under LH. We prove in ZFC that this condition actually ensures the existence of a proper totally dense subgroup of that contains an -bounded dense subgroup of (such an is necessarily pseudocompact). This answers two questions posed by Dikranjan and Shakhmatov (Proc. Amer. Math. Soc. 114 (1992), 1119-1129).