One of the most important contentions of the Rasch model of item analysis is that two tests of the same trait, having some items in common, can be linked together using a "linking constant" derived from the common items. This would be accomplished by administering both tests to a sample of testees, calibrating the items of the tests independently, and then linking the test by a linking constant which would be the difference between the average calibration of the common items on test one and the independently determined average calibration of the common items on test two. An important question regarding this linking procedure is whether the accuracy of the link is affected significantly when the items used for the linking represent a restricted range of difficulty relative to all items in the tests being linked. This paper empirically addresses this question with a variety of analyses using test results from mathematics tests administered to samples of fourth through seventh grade pupils. While the analyses varied with respect to the specific questions that they addressed, the overall conclusion was that for these tests, restriction in range of item difficultly did not present serious difficulties for test linking using the Rasch procedures. (Author/JKS)