In confining gauge theories in 3 and 4 dimensions, it is expected that at asymptotically large distances, the list of string tensions should be at most as large as the center of the gauge group. However, this characterization via center symmetry (or N-ality) seems incomplete; lattice simulations indicate that at intermediate distances, the list of string tensions is actually much larger. I will describe a lattice gauge model in 3 dimensions where a similar phenomenon takes place, and show that a non-invertible symmetry provides a natural explanation.