We have tested two methods of compensating environmental disturbances applicable to high-temperature superconducting quantum interference device (SQUID) systems operating in magnetically unshielded environments. For testing, we used first- and second-order axial electronic gradiometer setups with rf SQUID magnetometers operating at 77 K and base lines between 7 and 8 cm. The magnetometers were single-layer washer rf SQUIDs with bulk or thin-film magnetic flux concentrators in flip-chip geometry. The tested methods resulted in disturbance compensation levels comparable to those attained using electronically formed gradiometers. The white noise of the compensated magnetometers resulted in13.5 fT/cm &sqrt;Hzfor first-order and 22 fT/cm2&sqrt;Hzfor second-order compensation down to a few Hz. Common mode rejection was balanced to better than 10 000 for homogeneous fields and better than 200 for gradient fields with second-order compensation. ©1997 American Institute of Physics.