The past decade has seen frequent use of a modified nonlinear Schrödinger equation to describe ultrashort pulse propagation in materials where free-carrier plasmas are present. The optical contribution from the resulting free-current densities in this equation is often described using a classical Drude model. However, the ultimate form of this contribution in the modified nonlinear Schrödinger equation is somewhat inconsistent in the literature. We clarify this ambiguity by deriving the modified nonlinear Schrödinger equation from the classical wave equation containing a free-current density contribution. The Drude model is then used to obtain an expression for the complex free-carrier current density envelope with temporal dispersion corrections for ultrashort laser pulses. These temporal dispersion corrections to the current-density term differ, to our knowledge, from all other models in the literature in that they depend more sensitively on the value of the Drude free-carrier collision time. These corrections reduce to the current models in the literature for limiting cases. Theoretical analysis and computer simulations show that these differences can significantly affect the dynamic interactions of plasma absorption and plasma defocusing for materials with free-carrier collision times on the order of one optical cycle (or less) of the applied field.