Abstract: Morava $E$-theory is an important cohomology theory in chromatic homotopy theory. Using work of Ando, Hopkins, and Strickland, Rezk described the algebraic structure found in the homotopy of $K(n)$-local commutative $E$-algebras via a monad on $E_*$-modules that encodes all power operations. However, the construction does not see that the homotopy of a $K(n)$-local spectrum is $L$-complete (in the sense of Greenlees-May and Hovey-Strickland). We improve the construction to a monad on $L$-complete $E_*$-modules, and discuss some applications. Joint with Tobias Barthel.