Disjointification inequalities are proven for arbitrary martingale difference sequences and conditionally independent random variables of the form ${f_k\left(s\right)x_k\left(t\right)}_{k=1}ⁿ$, where $f_k$’s are independent and xk’s are arbitrary random variables from a symmetric space X on [0,1]. The main results show that the form of these inequalities depends on which side of L₂ the space X lies on. The disjointification inequalities obtained allow us to compare norms of sums of martingale differences and non-negative random variables with...