  In this work, a new approach to obtain a solenoidal Lipschitz truncation is
presented. More precisely, the goal of the truncation is to modify a function
$u \in W^{1,p}(\mathbb{R}^3,\mathbb{R}^3)$ that satisfies the additional
constraint $\mathrm{div}~ u=0$, such that its modification $\tilde{u}$ is in
$W^{1,\infty}(\mathbb{R}^3,\mathbb{R}^3)$ and still is divergence-free. We give
an alternative approach to Lipschitz truncation compared to previous works by
Breit, Diening & Fuchs (2012) and Breit, Diening & Schwarzacher (2013). The
ansatz pursued here allows a rather strict bound on the $W^{1,p}$ distance of
$u$ and $\tilde{u}$.
