Presented is a summary of studies by the LIGO Scientific Collaboration's Inspiral Analysis Group on the development of possible vetoes to be used in the evaluation of data from the first two LIGO science data runs. Numerous environmental monitor signals and interferometer control channels have been analysed in order to characterize the interferometers' performance. The results of studies on selected data segments are provided in this paper. The vetoes used in the compact binary inspiral analyses of LIGO's S1 and S2 science data runs are presented and discussed.