We use high–quality optical rotation curves of 9 low–luminosity disk galaxies to obtain the velocity profiles of the surrounding dark matter halos . We find that they increase linearly with radius at least out to the edge of the stellar disk , implying that , over the entire stellar region , the density of the dark halo is about constant . The properties of the mass structure of these halos are similar to those found for a number of dwarf and low surface brightness galaxies , but provide a more substantial evidence of the discrepancy between the halo mass distribution predicted in the Cold Dark Matter scenario and those actually detected around galaxies . We find that the density law proposed by Burkert ( 1995 ) reproduces the halo rotation curves , with halo central densities ( \rho _ { 0 } \sim 1–4 \times 10 ^ { -24 } g cm ^ { -3 } ) and core radii ( r _ { 0 } \sim 5–15 kpc ) scaling as \rho _ { 0 } \propto r _ { 0 } ^ { -2 / 3 } .