  Advantages and disadvantages of fixation of fundamental physical constants'
values for definition of SI units are considered. The case with a new
definition of the mass unit on the base of a fixed value of the Avogadro
constant is studied in detail. Criteria on choosing of a optimum FPC set with
fixed values for the redefinition of the SI units are suggested. The minimal
optimum FPC set that is consistent with the criteria is presented. The set
comprises the speed of light, the constant of the ground state hyperfine
transition of the caesium-133 atom, the Avogadro constant, the mass of the
carbon-12 atom and the absolute magnitude of the electron charge. Comment on
the redefinition of the kelvin is also made.
