  In many models of dusty objects in space the grains are assumed to be
composite or fluffy. However, the computation of the optical properties of such
particles is still a very difficult problem. We analyze how the increase of
grain porosity influences basic features of cosmic dust -- interstellar
extinction, dust temperature, infrared bands and millimeter opacity. Porous
grains can reproduce the flat extinction across the $3 - 8 \mkm$ wavelength
range measured for several lines of sight by {\it ISO} and {\it Spitzer}.
  Porous grains are generally cooler than compact grains. At the same time, the
temperature of very porous grains becomes slightly larger in the case of the
EMT-Mie calculations in comparison with the results found from the
layered-sphere model. The layered-sphere model predicts a broadening of
infrared bands and a shift of the peak position to larger wavelengths as
porosity grows. In the case of the EMT-Mie model variations of the feature
profile are less significant. It is also shown that the millimeter mass
absorption coefficients grow as porosity increases with a faster growth
occurring for particles with Rayleigh/non-Rayleigh inclusions. As a result, for
very porous particles the coefficients given by two models can differ by a
factor of about 3.
  It is found that an increase of porosity leads to an increase of extinction
cross sections at some wavelengths and a decrease at others depending on the
grain model. However, this behaviour is sufficient to reproduce the extinction
curve in the direction of the star $\sigma$ Sco using current solar abundances.
In the case of the star $\zeta$ Oph our model requires larger amounts of carbon
and iron in the dust-phase than is available.
