The angular momentum of galactic discs in semi-analytic models of galaxy formation is usually updated in time as material is accreted to the disc by adopting a constant dimensionless spin parameter and little attention is paid to the effects of accretion with misaligned angular momenta. These effects are the subject of this paper, where we adopt a Monte Carlo simulation for the changes in the direction of the angular momentum of a galaxy disc as it accretes matter based on accurate measurements from dark-matter haloes in the Millennium II simulation. In our semi-analytic model implementation, the flips seen in the dark-matter haloes are assumed to be the same for the cold baryons; however, we also assume that in the latter the flip also entails a difficulty for the disc to increase its angular momentum which causes the disc to become smaller relative to a no-flip case. This makes star formation to occur faster, especially in low-mass galaxies at all redshifts allowing galaxies to reach higher stellar masses faster. We adopt a new condition for the triggering of starbursts during mergers. As these produce the largest flips it is natural to adopt the disc instability criterion to evaluate the triggering of bursts in mergers instead of one based on mass ratios as in the original model. The new implementation reduces the average lifetimes of discs by a factor of ∼2, while still allowing old ages for the present-day discs of large spiral galaxies. It also provides a faster decline of star formation in massive galaxies and a better fit to the bright end of the luminosity function at z = 0.Instituto de Astrofísica de La PlataFacultad de Ciencias Astronómicas y Geofísicas