A dense plasma focus is being studied as a source of fusion neutrons. Lee and Serban noticed (IEEE Trans. Plasma Sci., vol. 24, no. 3, pp. 1101-1105, 1996) that neutron-optimized Mather-type plasma foci have an almost constant drive parameter I-0/(a root rho(0)). The origin of this parameter goes back to the 1960s. Recently, it has been pointed out that the constant value of the drive parameter means almost the same values of axial and radial velocities, ion temperatures, Alfven velocities, and magnetic energy per unit mass. Several physical mechanisms were suggested to explain the constant characteristic velocities in plasma foci. This paper presents the relation between the drive parameter and the rise rate of a current. The dependence of the drive parameter on plasma focus geometry is also derived. The obtained results are illustrated by neutron-optimized plasma foci with significantly higher drive parameters. Possible consequences on plasma focus research are mentioned.