We measured the threshold of visibility of a thin line against a solid background. The line colour differed from that of the background in only one of L*, C*, and h_ab. The twenty-seven background colours were distributed throughout colour space. We observed trends in the dependence of the threshold differences in C* and h_ab as functions of C* and h_ab of the background colour. We found our best quantitative agreement resulted from a C* and h_ab dependent colour difference formula, similar in spirit to the CIE94 colour difference metric, but with different parameters and weighting functions. Finally we simulated our geometry in input to an s-CIELAB implementation and found that s-CIELAB predicted our results quite well.