  We prove that all projective crepant resolutions of Nakajima quiver varieties
satisfying natural conditions are also Nakajima quiver varieties. More
generally, we classify the small birational models of many Geometric Invariant
Theory (GIT) quotients by introducing a sufficient condition for the GIT
quotient of an affine variety $V$ by the action of a reductive group $G$ to be
a relative Mori Dream Space. Two surprising examples illustrate that our new
condition is optimal. When the condition holds, we show that the linearisation
map identifies a region of the GIT fan with the Mori chamber decomposition of
the relative movable cone of $V /\!/_{\theta} G$. If $V/\!/_{\theta} G$ is a
crepant resolution of $Y\!\!:= V/\!/_{0} G$, then every projective crepant
resolution of $Y$ is obtained by varying $\theta$. Under suitable conditions,
we show that this is the case for quiver varieties and hypertoric varieties.
Similarly, for any finite subgroup $\Gamma\subset \mathrm{SL}(3,\mathbb{C})$
whose nontrivial conjugacy classes are all junior, we obtain a simple geometric
proof of the fact that every projective crepant resolution of
$\mathbb{C}^3/\Gamma$ is a fine moduli space of $\theta$-stable
$\Gamma$-constellations.
