  We discuss the main characteristic features in the heliospheric parameters
important for the GCR intensity modulation for the last three solar minima
(1986--1987, 1996--1997 and 2008--2009). The model for the GCR intensity
modulation is considered and the set of the model parameters is chosen which
allows the description of the observed GCR intensity distributions at the
moments of the maximum GCR intensity in two solar minima (1987 and 1997) normal
for the second half of the last century. Then we try to describe with the above
model and set of parameters the unusually soft GCR energy spectra at the
moments of the maximum GCR intensity in the last solar minimum between cycles
23 and 24 (2009). Our main conclusion is that the most simple way to do so is
to reduce the size of the modulation region and, probably, change the rigidity
dependence of the diffusion coefficient. The change of both parameters is
substantiated by the observations of the solar wind and heliospheric magnetic
field.
