One illustrative method disclosed herein includes the steps of forming a masking layer that covers a P-type transistor and exposes at least a gate cap layer of an N-type transistor, performing a first etching process through the masking layer to remove a portion of the gate cap of the N-type transistor so as to thereby define a reduced thickness gate cap layer for the N-type transistor, removing the masking layer, and performing a common second etching process on the P-type transistor and the N-type transistor that removes a gate cap layer of the P-type transistor and the reduced thickness gate cap of the N-type transistor.