  We report on the results of a comparative investigation of highly dense bulk
MgB$_2$ samples prepared by three methods: (i) hot deformation; (ii) high
pressure sintering; and (iii) mechanical alloying of Mg and B powders with
subsequent hot compaction. All types of samples were studied by
ac-susceptibility, dc-magnetization and resistivity measurements in magnetic
fields up to $\mu_0H=160$ kOe. A small but distinct anisotropy of the upper
critical field $H_{c2}^{a,b}/H_{c2}^{c}\sim1.2$ connected with some texture of
MgB$_2$ grains was found for the hot deformed samples. The samples prepared by
high pressure sintering as well as by mechanical alloying show improved
superconducting properties, including high upper critical fields $H_{c2}$
($\mu_0H_{c2}(0)\sim23$ T), irreversibility fields $H_{irr}$ which are strongly
shifted towards higher values $H_{irr}(T)\sim0.8H_{c2}(T)$ and high critical
current $J_c$ ($J_c=10^5$ A/cm$^2$ at 20 K and 1 T).
