  We present a new method to extract cosmological constraints from weak lensing
(WL) peak counts, which we denote as `the hierarchical algorithm'. The idea of
this method is to combine information from WL maps sequentially smoothed with a
series of filters of different size, from the largest down to the smallest,
thus increasing the cosmological sensitivity of the resulting peak function. We
compare the cosmological constraints resulting from the peak abundance measured
in this way and the abundance obtained by using a filter of fixed size, which
is the standard practice in WL peak studies. For this purpose, we employ a
large set of WL maps generated by ray-tracing through N-body simulations, and
the Fisher matrix formalism. We find that if low-S/N peaks are included in the
analysis (S/N ~ 3), the hierarchical method yields constraints significantly
better than the single-sized filtering. For a large future survey such as
Euclid or LSST, combined with information from a CMB experiment like Planck,
the results for the hierarchical (single-sized) method are: \Delta n=0.0039
(0.004); \Delta \Omega m=0.002 (0.0045); \Delta \sigma 8=0.003 (0.006); \Delta
w=0.019 (0.0525). This forecast is conservative, as we assume no knowledge of
the redshifts of the lenses, and consider a single broad bin for the redshifts
of the sources. If only peaks with S/N >= 6 are considered, then there is
little difference between the results of the two methods. We also examine the
statistical properties of the hierarchical peak function: Its covariance matrix
has off-diagonal terms for bins with S/N <= 6 and aperture mass of M < 3 x
1e+14 Ms/h, the higher bins being largely uncorrelated and therefore well
described by a Poisson distribution.
