  We introduce a measure called width, quantifying the amount of nondeterminism
in automata. Width generalises the notion of good-for-games (GFG) automata,
that correspond to NFAs of width 1, and where an accepting run can be built
on-the-fly on any accepted input. We describe an incremental determinisation
construction on NFAs, which can be more efficient than the full powerset
determinisation, depending on the width of the input NFA. This construction can
be generalised to infinite words, and is particularly well-suited to coB\"uchi
automata. For coB\"uchi automata, this procedure can be used to compute either
a deterministic automaton or a GFG one, and it is algorithmically more
efficient in the last case. We show this fact by proving that checking whether
a coB\"uchi automaton is determinisable by pruning is NP-complete. On finite or
infinite words, we show that computing the width of an automaton is
EXPTIME-complete. This implies EXPTIME-completeness for multipebble simulation
games on NFAs.
