The Engset model has been extensively studied and widely used for blocking probability evaluation in telecommunications networks. In 1957, J.W. Cohen considered two generalizations of the Engset model: 1) permitting the distributions of the holding time and interarrival time to differ from source to source; 2) permitting the idle time distribution to depend on whether or not the previous call was successful. He derived the call and time congestions for the first generalization, however, he simply posed the second generalization as a problem. In a leading teletraffic text by Syski, the call and time congestions are approximated for the second generalization, though it appears that Syski has overlooked that his results are in fact an approximation. In this paper, we point out Syski's apparent oversight, we improve the accuracy of his approximation, and we provide an efficient algorithm for its numerical computation and prove its convergence