We have measured current-voltage characteristics at liquid-helium temperature and for magnetic fields up to 7T(parallel to the current flow) for three similar asymmetric GaAs/AlAs double-barrier structures, all of which possess large phonon-assisted tunnelling currents. Confined longitudinal optical (LO) phonons in the GaAs well layer and LO-like symmetric interface phonons treated within a dielectric continuum picture suffice to account for the measured currents. Phonon-assisted tunnelling current levels as well as magnetotunnelling data are found to depend sensitively on well and barrier widths.