The Sausage Catastrophe of J. Wills (1983) is the observation that in \(d=3\) and \(d=4\) , the densest packing of n spheres in \(\mathbb {R}^{d}\) is a sausage for small values of n and jumps to a full-dimensional packing for large n without passing through any intermediate dimensions. Let \(n_{d}^{*}\) be the smallest value of n for which the densest packing of n spheres in \(\mathbb {R}^{d}\) is full-dimensional and \(N_{d}^{*}\) be the smallest value of N for which the densest packing of N spheres in \(\mathbb {R}^{d}\) is full-dimensional for all \(N\ge N_{d}^{*}\) . We extend the work of Gandini and Zucco (1992) to obtain new upper bounds of \(n_{4}^{*}\le 338,\!196\) and \(N_{4}^{*}\le 516,\!946\) . Some lengthy and repetitive components of the proof of the latter result were obtained using interval arithmetic.