For an ordinal $$\varepsilon $$ ε , I introduce a variant of the notion of subcompleteness of a forcing poset, which I call $$\varepsilon $$ ε -subcompleteness, and show that this class of forcings enjoys some closure properties that the original class of subcomplete forcings does not seem to have: factors of $$\varepsilon $$ ε -subcomplete forcings are $$\varepsilon $$ ε -subcomplete, and if $$\mathbb {P}$$ P and $$\mathbb {Q}$$ Q are forcing-equivalent notions, then $$\mathbb {P}$$ P is $$\varepsilon $$ ε -subcomplete iff $$\mathbb {Q}$$ Q is. I formulate a Two Step Theorem for $$\varepsilon $$ ε -subcompleteness and prove an RCS iteration theorem for $$\varepsilon $$ ε -subcompleteness which is slightly less restrictive than the original one, in that its formulation is more careful about the amount of collapsing necessary. Finally, I show that an adequate degree of $$\varepsilon $$ ε -subcompleteness follows from the $$\kappa $$ κ -distributivity of a forcing, for $$\kappa >\omega _1$$ κ>ω1 .