Recently, Avgustinovich, Kitaev, and Taranenko defined five types of (k,ℓ)-crucial permutations, which are maximal permutations that do not contain an increasing subsequence of length k or a decreasing subsequence of length ℓ. Further, Avgustinovich, Kitaev, and Taranenko began the enumeration of the (k,ℓ)-crucial permutations of the minimal length and the next minimal length and the (k,3)-crucial permutations of all lengths for each of the five types of (k,ℓ)-crucial permutations. In this paper, we complete the enumeration that Avgustinovich, Kitaev, and Taranenko began.