© 2015 American Physical Society. We have studied the structure, magnetic, and transport properties of copper-substituted iron telluride. Our results extend the range of copper substitution to 60% substitution per formula unit, which is far beyond previously stated solubility limits. Substitution of copper into antiferromagnetic iron telluride is found to suppress the signatures of the low-temperature transitions in susceptibility and resistance measurements, giving rise to an insulating, spin-glass state. Upon increasing the copper substitution from 4% to 6%, short-range antiferromagnetic order appears followed by the combined magnetic and structural transition at a lower temperature, although the magnetic order is ultimately not resolution limited with a correlation length of 250 Å in the 6% Cu-substituted sample, in contrast to the magnetic order of the 4% copper-substituted sample, which is resolution limited. Upon warming the 6% Cu-substituted sample in the presence of a 5 T magnetic field oriented along the b axis, magnetic and structural phase transitions are observed at a temperature much lower than those of the magnetic and structural transitions which occur in zero field. Furthermore, these transitions are absent upon cooling in this field. We discuss the field results in the most general terms possible, including possible random field effects.