Accretion in the nuclei of active galaxies may occur chaotically. This can produce accretion discs which are counter-rotating or strongly misaligned with respect to the spin of the central supermassive black hole (SMBH), or the axis of a close SMBH binary. Accordingly we consider the cancellation of angular momentum in accretion discs with a significant change of plane (tilt) between inner and outer parts. We estimate analytically the maximum accretion rate through such discs and compare this with the results of smoothed particle hydrodynamics simulations. These suggest that accretion rates on to SMBH may be larger by factors of ≳100 if the disc is internally tilted in this way rather than planar. This offers a natural way of driving the rapid growth of SMBH and the coalescence of SMBH binaries.