  An \emph{$\omega$-admissible almost complex structure} on a $2n$-dimensional
symplectic manifold $(M,\omega)$ is a $\omega$-calibrated almost complex
structure $J$ admitting a nowhere vanishing $\bar{\partial}_J$-closed
$(n,0)$-form $\psi$. After giving some examples we consider the moduli space of
admissible almost complex structures and we study infinitesimal deformations.
As special case, we write down explicit computations for the complex torus.
