Let T be a spherical completely hyperexpansive m-variable weighted shift on a complex, separable Hilbert space H and let T^s denote its spherical Cauchy dual. We obtain the hyperexpansivity analog of the structure theorem of Olin-Thomson for the C*-algebra C*(T) generated by T, under the natural assumption that T^s is commuting. If, in addition, the defect operator I - T₁T*₁ - ... - T_mT*_m is compact then we ensure exactness of the sequence of C*-algebras 0 → C(H) → C*(T) → C(σ_ap(T)) → 0, where C(H) stands for the ideal of compact operators on H, and π : C*(T) → C(σ_ap(T)) is the unital *-homomorphism defined by π(T_i)= z_i (i=1, ..., m). This unifies and generalizes the results of Coburn, 1973/74 and Arveson, 1998. We further illustrate our results by exhibiting a one parameter family F of spherical completely hyperexpansive 2-tuples T_νλ acting on P²(μ_λ) (1 ≦ λ ≦ 2), where dμ_λ:= dν_λ dσ, ν_λ is a probability measure on [0, 1], and σ is the normalized surface area measure on the unit sphere ∂B. Interestingly, within the family F, the Szegö 2-shift T_ν1 and the Drury-Arveson 2-shift T_ν2 occupy the extreme positions. We would like to emphasize that T_νλ is unitarily equivalent to the multiplication operator tuples in P²(μ_λ) if and only if λ =1.