  We present the HI data for 5 spiral galaxies that, along with their Halpha
rotation curves, are used to derive the distribution of dark matter within
these objects. A new method for extracting rotation curves from HI data cubes
is presented; this takes into account the existence of a warp and minimises
projection effects. The rotation curves obtained are tested by taking them as
input to construct model data cubes that are compared to the observed ones: the
agreement is excellent. On the contrary, the model data cubes built using
rotation curves obtained with standard methods, such as the first-moment
analysis, fail the test. The HI rotation curves agree well with the Halpha
data, where they coexist. Moreover, the combined Halpha + HI rotation curves
are smooth, symmetric and extended to large radii.
  The rotation curves are decomposed into stellar, gaseous and dark matter
contributions and the inferred density distribution is compared to various mass
distributions: dark haloes with a central density core, $\Lambda$ Cold Dark
Matter ($\Lambda$CDM) haloes (NFW, Moore profiles), HI scaling and MOND. The
observations point to haloes with constant density cores of size $r_{core} \sim
r_{opt}$ and central densities scaling approximately as $\rho_0 \propto
r_{core}^{-2/3}$. $\Lambda$CDM models (which predict a central cusp in the
density profile) are in clear conflict with the data. HI scaling and MOND
cannot account for the observed kinematics: we find some counter-examples.
