  We deduce conditional $L_p$-estimates for the variation of a solution of a
BSDE. Both quadratic and sub-quadratic types of BSDEs are considered, and using
the theory of weighted bounded mean oscillation we deduce new tail estimates
for the solution $(Y,Z)$ on subintervals of $[0,T]$. Some new results for the
decoupling technique introduced in \cite{jossain} are obtained as well and some
applications of the tail estimates are given.
