Recent investigations have shown that approximations of certain channels by the linear deterministic model (LDM) are sub-optimal in some cases. Replacing the LDM by a more sophisticated deterministic model possibly results in improvements of previous results. An example is use of the lower triangular deterministic model (LTDM) to replace the LDM. Due to the integrated dependence on the fine channel gains, results can be obtained which were not previously possible. In this paper, we investigate the IMAC under the approximation of this refined model. It was previously demonstrated, that multi-user gain is present in the conventional deterministic IMAC model. However, the capacity could be shown just for discrete points due to limitations of the approximation model. In this paper, we propose a scheme for the new approximation model, which reaches the upper bound completely and therefore provides the sum-capacity. Moreover, the scheme itself has a much more simplistic structure.