Principles Weaker than BD-N

BD-N is a weak principle of constructive analysis. Several interesting principles implied by BD-N have already been identified, namely the closure of the anti-Specker spaces under product, the Riemann Permutation Theorem, and the Cauchyness of all partially Cauchy sequences. Here these are shown to be strictly weaker than BD-N, yet not provable in set theory alone under constructive logic.