  The elegant `no short hair' theorem states that, if a spherically-symmetric
static black hole has hair, then this hair must extend beyond 3/2 the horizon
radius. In the present paper we provide evidence for the failure of this
theorem beyond the regime of spherically-symmetric static black holes. In
particular, we show that rotating black holes can support extremely short-range
stationary scalar configurations (linearized scalar `clouds') in their exterior
regions. To that end, we solve analytically the Klein-Gordon-Kerr-Newman wave
equation for a linearized massive scalar field in the regime of large scalar
masses.
