  We construct two linear filtering techniques based on weak gravitational
lensing to constrain the inner slope $\alpha$ of the density profile of
dark-matter halos. Both methods combine all available information into an
estimate of this single number. Under idealised assumptions, $\alpha$ is
constrained to ~15% if the halo concentration c is known, and to < 30% if not.
We argue that the inevitable degeneracy between density-profile slope and halo
concentration cannot be lifted under realistic conditions, and show by means of
Fisher-matrix methods which linear combination of $\alpha$ and c is best
constrained by our filtering of lensing data. This defines a new parameter,
called P1, which is then constrained to ~15% for a single massive halo. If the
signals of many halos can be stacked, their density profiles should thus be
well constrained by the linear filters proposed here with the advantagebe
insensitive to the cluster substructures.
