We measured 73.5% correct just noticeable differences (JNDs) in bar orientation with the method of constant stimuli and with a Wetherill and Levitt staircase procedure, using a total of 25 cats. For the same number of trials per threshold assessment, the variability of the threshold remained independent of the testing method used. However, the JNDs measured using the method of constant stimuli were significantly influenced by the range of the orientation differences (ODs) utilized for measuring the JND. This effect was particularly large in incompletely trained cats, but it also was significant in extensively trained subjects. On the other hand, staircase threshold measurements were not affected by the starting OD, independently of how well the animals had been trained. This shows that the staircase procedure is a more efficient instrument with which to measure JNDs in orientation than is the method of constant stimuli. With the staircase procedure, we found that the JNDs measured at oblique reference orientations did not exceed those measured at principal reference orientations (no oblique effect). Two earlier studies from this laboratory using the method of constant stimuli did report an oblique effect. Our data suggest that this oblique effect might stem from a less efficient training at the right oblique reference orientation in these studies, combined with a relatively inefficient testing procedure such as the constant stimuli method.