New observations of H I rotation curves at the Very Large Array have uncovered two galaxies with rotation curves declining between 1 and 3 optical radii. The velocity decrease is large, more than 50 km s-1 (approximately 25% of the maximum rotation velocity), and is present on both sides of the galaxies; projection effects can be ruled out. We interpret the decrease in rotation velocity as an indication of a large ratio of luminous to dark mass in the luminous regions of these systems. An analysis of the current observations combined with rotation curves from the literature shows a clear correlation between peak circular velocity of a galaxy, its central surface brightness and the slope of the rotation curve in the outer parts. This correlation indicates a weakening of the well-known conspiracy between luminous and dark matter, and may provide evidence in favor of the idea that dark matter is baryonic. Although we do not sample the full morphological Hubble sequence, a strong correlation between slope of the rotation curve and morphological type is found. This result seems to support earlier suggestions that the ratio between the mass in dark and luminous matter might be the critical parameter that controls the Hubble sequence.