We say a permutation π=π_1π_2...π_n in the symmetric group S_n has a peak at index i if π_i-1<π_i>π_i+1 and we let P(π)={i ∈{1, 2, ..., n} i is a peak of π}. Given a set S of positive integers, we let P (S; n) denote the subset of S_n consisting of all permutations π, where P(π) =S. In 2013, Billey, Burdzy, and Sagan proved |P(S;n)| = p(n)2^n- S-1, where p(n) is a polynomial of degree (S)- 1. In 2014, Castro-Velez et al. considered the Coxeter group of type B_n as the group of signed

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... s on n letters and showed that P_B(S;n)=p(n)2^2n-|S|-1 where p(n) is the same polynomial of degree (S)-1. In this paper we partition the sets P(S;n) ⊂S_n studied by Billey, Burdzy, and Sagan into subsets of P(S;n) of permutations with peak set S that end with an ascent to a fixed integer k or a descent and provide polynomial formulas for the cardinalities of these subsets. After embedding the Coxeter groups of Lie type C_n and D_n into S_2n, we partition these groups into bundles of permutations π_1π_2 ...π_n|π_n+1...π_2n such that π_1π_2...π_n has the same relative order as some permutation σ_1σ_2...σ_n ∈S_n. This allows us to count the number of permutations in types C_n and D_n with a given peak set S by reducing the enumeration to calculations in the symmetric group and sums across the rows of Pascal's triangle.