We obtain new bounds, pointwise and on average, for Dedekind sums \({\textsf{s}}(\lambda ,p)\) 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 recent results of the second and third author to study these correlations.
