We discuss a notion of forcing that characterizes enumeration 1-genericity, and we investigate the immunity, lowness, and quasiminimality properties of enumeration 1-generic sets and their degrees. We construct an enumeration operator Δ such that, for any A, the set ΔA is enumeration 1-generic and has the same jump complexity as A. We deduce from this and other recent results from the literature that not only does every degree a bound an enumeration 1-generic degree b such that a'=b', but also that, (...) if a is nonzero, then we can find such b satisfying 0eshrink)

We show that there exist downwards properly $\Sigma _{2}^{0}$ (in fact noncuppable) e-degrees that are not high. We also show that every high e-degree bounds a noncuppable e-degree.