It is shown that if \kappa is an uncountable successor cardinal in L\lbrack 0^\sharp\rbrack, then there is a normal tree \mathbf{T} \in L \lbrack 0^\sharp\rbrack of height \kappa such that 0^\sharp \not\in L\lbrack\mathbf{T}\rbrack. Yet \mathbf{T} is <\kappa-distributive in L\lbrack 0^\sharp\rbrack. A proper class version of this theorem yields an analogous L\lbrack 0^\sharp\rbrack-definable tree such that distinct branches in the presence of 0^\sharp collapse the universe. A heretofore unutilized method for constructing in L\lbrack 0^\sharp\rbrack generic objects for certain L-definable forcings and "exotic sequences", combinatorial principles introduced by C. Gray, are used in constructing these trees.