The authors derive sharp Rosenthal-type inequalities for moments of sums \(X_1+\cdots+X_n\) of independent random variables under various conditions on the summands. For example, they consider the situation in which each \(X_j\) is equal in distribution to \(R_jV\) for a non-negative random variable \(R_j\) independent of \(V\), generalising the symmetry condition in the usual Rosenthal inequality. In this case the authors give an explicit expression for the optimal constant \(\mathbf{C}_{p,V}\) in the inequality \[ \left\lVert\sum_{j=1}^nX_j\right\rVert_p\leq\mathbf{C}_{p,V}\max\left\{\left(\sum_{j=1}^n\left\lVert X_j\right\rVert_2^2\right)^{1/2},\left(\sum_{j=1}^n\left\lVert X_j\right\rVert_p^p\right)^{1/p}\right\}\,. \] In the cases where the \(X_j\) are either log-concave or symmetric with \(\mathbb{P}(|X_j|>t)\) log-concave, the authors identify the extremal distributions in Rosenthal-type inequalities when the moments of the \(X_j\) are individually constrained.