  We prove noncommutative Khintchine inequalities for all interpolation spaces
between $L_p$ and $L_2$ with $p<2$. In particular, it follows that Khintchine
inequalities hold in $L_{1,\infty}$. Using a similar method, we find a new
deterministic equivalent for the $RC$-norm in all interpolation spaces between
$L_p$-spaces which unifies the cases $p > 2$ and $p < 2$. It produces a new
proof of Khintchine inequalities for $p<1$ for free variables. To complete the
picture, we exhibit counter-examples which show that neither of the usual
closed formulas for Khintchine inequalities can work in $L_{2,\infty}$. We also
give an application to martingale inequalities.
