Multinomial-response models are available that correspond implicitly to tests in which a total score is computed as the sum of polytomous item scores. For these models, joint and conditional estimation may be considered in much the same way as for the Rasch model for right-scored tests. As in the Rasch model, joint estimation is only attractive if both the number of items and the number of examinees are large, while conditional estimation can be employed for a large number of examinees whether or not the number of items is large. In neither case is computation difficult given currently available computers. Large-sample results favor use of conditional estimation, although some use of joint estimation can be contemplated if the number of items is large.