Summary: Generalising an earlier result due to the present author [Commun. Fac. Sci. Univ. Ankara, Sér. A 1 30, 7-16 (1981; Zbl 0449.42001)], it is shown as a particular case that the degree of approximation of functions \(f\in Lip \alpha\) \((0<\alpha \leq 1)\) by \((E,q)\)-means of its Fourier series in sup-norm is \(O\{n^{-\alpha}\log n\}\).