In a LCDM cosmology, the baryonic Tully-Fisher relation (BTFR) is expected to show significant intrinsic scatter resulting from the mass-concentration relation of dark matter halos and the baryonic-to-halo mass ratio. We study the BTFR using a sample of 118 disc galaxies (spirals and irregulars) with data of the highest quality: extended HI rotation curves (tracing the outer velocity) and Spitzer photometry at 3.6 $mu$m (tracing the stellar mass). Assuming that the stellar mass-to-light ratio (M*/L) is nearly constant at 3.6 $mu$m, we find that the scatter, slope, and normalization of the BTFR systematically vary with the adopted M*/L. The observed scatter is minimized for M*/L > 0.5, corresponding to nearly maximal discs in high-surface-brightness galaxies and BTFR slopes close to ~4. For any reasonable value of M*/L, the intrinsic scatter is ~0.1 dex, below general LCDM expectations. The residuals show no correlations with galaxy structural parameters (radius or surface brightness), contrary to the predictions from some semi-analytic models of galaxy formation. These are fundamental issues for LCDM cosmology.