We study a family of higher-twist Regge trajectories in 𝒩=4 supersymmetric Yang-Mills theory using the quantum spectral curve. We explore the many-sheeted Riemann surface connecting the different trajectories and show the interplay between the degenerate nonlocal operators known as (near-)horizontal trajectories. We resolve their degeneracy analytically by computing the first nontrivial order of the Regge intercept at weak coupling, which exhibits new behavior: It depends linearly on the coupling. This is consistent with our numerics, which interpolate all the way to strong coupling.