We describe a procedure to compute a projection of \(w \in ℝ^n\) into the intersection of the so-called zero-norm ball \(k B_0\) of radius \(k\), i.e., the set of \(k\)-sparse vectors, with a box centered at a point of \(k B_0\). The need for such projection arises in the context of certain trust-region methods for nonsmooth regularized optimization. Although the set into which we wish to project is nonconvex, we show that a solution may be found in \(O(n \log(n))\) operations. We describe our Julia implementation and illustrate our procedure in the context of two trust-region methods for nonsmooth regularized optimization.