We investigate the effects of halo ellipticity and alignment with larger-scale structure on the galaxy correlation function. We base our analysis on the galaxy formation models of Guo et al. (2011), run on the Millennium Simulations. We quantify the importance of these properties of the galaxy distribution by randomizing the angular positions of satellite galaxies within haloes, either coherently or individually, while keeping the distance to their respective central galaxies fixed. We find that the effect of disrupting the alignment with larger-scale structure is a ~2 per cent decrease in the galaxy correlation function around r=1.8 Mpc/h. Sphericalizing the ellipsoidal distributions of galaxies within haloes decreases the correlation function by up to 20 per cent for r<1 Mpc/h. Similar results apply to power spectra and redshift-space correlation functions. Models such as those based on the Halo Occupation Distribution, which adopt a spherically averaged profile for the galaxy distributions within haloes, will therefore significantly underestimate the clustering on sub-Mpc scales.