A system for minimizing non-integral vibrations in rotor blades located in a compressor section of a gas turbine engine includes a casing having a plurality of bleed slots, at least one of the bleed slots being located in close proximity to a row of rotor blades, a plurality of structural ligaments, at least one of the structural ligaments extending between two adjacent ones of the bleed slots; and a channel for reducing the height of at least one of the structural ligaments so as to minimize the non-integral vibrations in the rotor blades in the row.