The goal of this paper is to find better ways to estimate the internal consistency reliability of scores on tests with a specific type of design that are often encountered in practice: tests with constructed-response items clustered into sections that are not parallel or tau-equivalent, and one of the sections has only one item. To estimate the reliability of scores on this kind of test, we propose a two-step approach (denoted as CA_STR) that first estimates the reliability of scores on the section with a single item using the correction for attenuation method and then estimates the reliability of scores on the whole test using the stratified coefficient alpha. We compared the CA_STR method with three other reliability estimation approaches under various conditions using both real and simulated data. We found that overall, the CA_STR method performed the best and it was easy to implement.