  We study the class of noncommutative theories in $d$ dimensions whose spatial
coordinates $(x_i)_{i=1}^d$ can be obtained by performing a smooth change of
variables on $(y_i)_{i=1}^d$, the coordinates of a standard noncommutative
theory, which satisfy the relation $[y_i, y_j] = i \theta_{ij}$, with a
constant $\theta_{ij}$ tensor. The $x_i$ variables verify a commutation
relation which is, in general, space-dependent. We study the main properties of
this special kind of noncommutative theory and show explicitly that, in two
dimensions, any theory with a space-dependent commutation relation can be
mapped to another where that $\theta_{ij}$ is constant.
