  We study the stability of the dislocation-free Bragg glass phase in a layered
geometry consisting of coupled parallel planes of d=1+1 vortex lines lying
within each plane, in the presence of impurity disorder. Using renormalization
group, replica variational calculations and physical arguments we show that at
temperatures $T<T_G$ the 3D Bragg glass phase is always stable for weak
disorder. It undergoes a weakly first order transition into a decoupled 2D
vortex glass upon increase of disorder.
