  We study crossing-free grid morphs for planar tree drawings using 3D. A morph
consists of morphing steps, where vertices move simultaneously along
straight-line trajectories at constant speeds. A crossing-free morph is known
between two drawings of an $n$-vertex planar graph $G$ with $\mathcal{O}(n)$
morphing steps and using the third dimension it can be reduced to
$\mathcal{O}(\log n)$ for an $n$-vertex tree [Arseneva et al.\ 2019]. However,
these morphs do not bound one practical parameter, the resolution. Can the
number of steps be reduced substantially by using the third dimension while
keeping the resolution bounded throughout the morph? We answer this question in
an affirmative and present a 3D non-crossing morph between two planar grid
drawings of an $n$-vertex tree in $\mathcal{O}(\sqrt{n} \log n)$ morphing
steps. Each intermediate drawing lies in a $3D$ grid of polynomial volume.
