  Let $V(T)$ denote the number of sign changes in $\psi(x) - x$ for $x\in[1,
T]$. We show that $\liminf_{\;T\rightarrow\infty} V(T)/\log T \geq
\gamma_{1}/\pi + 1.867\cdot 10^{-30}$, where $\gamma_{1} = 14.13\ldots$ denotes
the ordinate of the lowest-lying non-trivial zero of the Riemann zeta-function.
This improves on a long-standing result by Kaczorowski.
