  We obtain new bounds, pointwisely and on average, for Dedekind sums
$\mathsf{s}(\lambda,p)$ modulo a prime $p$ with $\lambda$ of small
multiplicative order $d$ modulo $p$. Assuming the infinitude of Mersenne
primes, the range of our results is optimal. Moreover, we relate high moments
of $L(1,\chi)$ over subgroups of characters to some correlations of Dedekind
sums and use our recent results to study these correlations.
