  We consider a smooth system of the form $\dot q=f_0(q)+\sum\limits_{i=1}^k
u_i f_i(q)$, $q\in M,\ u_i\in\mathbb R,$ and study controllability issues on
the group of diffeomorphisms of $M$. It is well-known that the system can
arbitrarily well approximate the movement in the direction of any Lie bracket
polynomial of $f_1,\ldots,f_k$. Any Lie bracket polynomial of $f_1,\ldots,f_k$
is good in this sense. Moreover, some combinations of Lie brackets which
involve the drift term $f_0$ are also good but surely not all of them. In this
paper we try to characterize good ones and, in particular, all universal good
combinations, which are good for any nilpotent truncation of any system.
