A combustor for a combustion turbine engine that includes: a chamber defined by an outer wall and forming a channel between windows defined through the outer wall toward a forward end of the chamber and at least one fuel injector positioned toward an aft end of the chamber; and a multilayer screen filter comprising at least two layers of screen over at least a portion of the windows and at least one layer of screen over the remaining portion of the windows. The windows include a forward end and a forward portion, and an aft end and an aft portion. The multilayer screen filter is positioned over the windows such that, in operation, a supply of compressed air entering the chamber through the windows passes through at least one layer of screen. The multilayer screen filter is configured such that the aft portion of the windows include at least two layers of screen, and the forward portion of the windows includes one less layer of screen than the aft portion of the windows.