  We study the properties of fundamental physical constants using the threefold
classification of dimensional constants proposed by J.-M. L{\'e}vy-Leblond:
constants of objects (masses, etc.), constants of phenomena (coupling
constants), and "universal constants" (such as $c$ and $\hbar$). We show that
all of the known "natural" systems of units contain at least one non-universal
constant. We discuss the possible consequences of such non-universality, e.g.,
the dependence of some of these systems on the number of spatial dimensions. In
the search for a "fully universal" system of units, we propose a set of
constants that consists of $c$, $\hbar$, and a length parameter and discuss its
origins and the connection to the possible kinematic groups discovered by
L{\'e}vy-Leblond and Bacry. Finally, we give some comments about the
interpretation of these constants.
