Let X be a \(T_ i\)-space, \(i\leq 2\). We define the \(T_ i\)-pseudoweight of X, \(\psi_ i(X)\), to be the least weight of a coarser \(T_ i\) topology on X. \textit{G. M. Reed} and \textit{P. L. Zenor} [Bull. Am. Math. Soc. 80, 879-880 (1974; Zbl 0293.54026)] have shown that if X is a Moore space, and \(| X| \leq 2^{\omega}\), then \(\psi_ 1(X)=\omega\), but there is a Moore space, X, such that \(\psi_ 2(X)=w(X)=| X| =\omega_ 1\). Theorem 1: If X is metric, \(\psi_ 0(X)=\psi_ 2(X)=\log w(X)\), where log \(\kappa\) \(=\min \{\lambda: 2^{\lambda}\geq \kappa \}\). Theorem 2: If X is compact and \(T_ 2\), then \(\psi_ 1(X)=\psi_ 2(X)=w(X)\) (but it is possible to have \(\psi_ 0(X)=\log w(X)