A testlet is a cluster of items that share a common passage, scenario, or other context. These items might measure something in common beyond the trait measured by the test as a whole; if so, the model for the item responses should allow for this testlet trait. But modeling testlet effects that are negligible makes the model unnecessarily complicated and risks capitalization on chance, increasing the error in parameter estimates. Checking each testlet to see if the items within the testlet share something beyond the primary trait could therefore be useful. This study included (a) comparison between a model with no testlets and a model with testlet "g," (b) comparison between a model with all suspected testlets and a model with all suspected testlets "except" testlet "g," and (c) a test of essential unidimensionality. Overall, Comparison b was most useful for detecting testlet effects. Model comparisons based on information criteria, specifically the sample-size adjusted Bayesian Information Criteria (SSA-BIC) and BIC, resulted in fewer false alarms than statistical significance tests. The test of essential unidimensionality had true hit rates and false alarm rates similar to the SSA-BIC when the testlet effect was zero for all testlets except the studied testlet. But the presence of additional testlet effects in the partitioning test led to higher false alarm rates for the test of essential unidimensionality. (Contains 4 tables, 3 figures, and 2 notes.)