Suppose G is a subgroup of the reduced abelian p-group A. The following two dual results are proved: (∗) If A/G is countable and G is an almost totally projective group, then A is an almost totally projective group. (∗∗) If G is countable and nice in A such that A/G is an almost totally projective group, then A is an almost totally projective group. These results somewhat strengthen theorems due to Wallace (J. Algebra, 1971) and Hill (Comment. Math. Univ. Carol., 1995), respectively.