  It is proved that bounded solutions of modified ($\theta$-twisted)
cohomological equations for expanding circle maps are $\theta$-H\"{o}lder
continuous but are not $(\theta+\gamma)$-H\"{o}lder continuous for every
$\gamma>0$ at almost every point. This gives new examples of "nonlinear"
Weierstrass-like functions for which the optimal \holder exponent at most
points is known.
