The DIMTEST statistical procedure was used in a confirmatory manner to explore the dimensionality structures of three kinds of achievement tests: multiple-choice tests, constructed-response tests, and tests combining both formats. The DIMTEST procedure is based on estimating conditional covariances of the responses to the item pairs. The analysis was conducted on the results from the joint administration of the Constructed-Response Supplement to the Iowa Tests of Basic Skills and Form M of the Iowa Tests of Basic Skills, using samples of 952 seventh graders and 882 eighth graders for the language tests, and 889 seventh graders and 918 eighth graders for the mathematics tests. Three potential sources of dimensional distinctness among items in the tests, caused by item format, item content, and item location, were investigated. The results differed for language and mathematics achievement tests, in part because the tests were dissimilar with regard to content composition and the number of items in the whole tests as well as subtests that were analyzed. The Poly-DIMTEST analysis presented provides evidence of dimensional heterogeneity of tests intended to provide assessments that are balanced with respect to the content composition of a targeted construct. The analysis also suggests that combining items of different formats may introduce additional complexity into the dimensionality structure of the composite test. (Contains 1 figure, 8 tables, and 31 references.) (SLD)