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Let a(n) be the minimum number of ideal hyperbolic tetrahedra necessary to construct a finite volume n-cusped hyperbolic 3-manifold, orientable or not. Let ~ror(n) be the corresponding number when we restrict ourselves to orientable manifolds. The correct values of a(n) and aor(n ) and the corresponding manifolds are given for n = 1, 2, 3, 4, and 5. We then show that 2n -1 < a(n) < tror(n ) < 4n -4 for n _ 5 and that Oor(n ) >_ 2n for all n.doi:10.1007/bf02574680 fatcat:rqe4jcpis5cpvfeq6bedmkmfcy