We investigate a linearly polarized, plane wave electromagnetic step function modulated sine wave pulse traveling through an isotropic, homogeneous, lossy plasma with dielectric permittivity described by the Drude model. The results of this investigation extend the useful frequency domain below the plasma cutoff frequency. An asymptotic method of analysis is used to provide a closed-form approximation to the integral representation of the propagated pulse that is valid for all input carrier frequencies. This closed-form expression is the sum of its three asymptotic component fields: the Sommerfeld precursor, the Brillouin precursor and the signal contribution. These expressions reveal that, because of conductivity, each field component attenuates exponentially with distance at its own characteristic rate and that, for sufficiently large propagation distance, the Sommerfeld precursor will be the dominant contribution to the field. However, a study of the penetration capability of each field component shows that, for a large enough propagation distance with carrier frequencies below cutoff, the Brillouin precursor decays algebraically as z−2 with a minimal exponential attenuation with propagation distance while the Sommerfeld precursor decays at a rate that approaches a z−3/4 algebraic decay. Optimal signal penetration through a finite distance of a lossy plasma medium, for either radar imaging, remote sensing, or communication applications, may then be realized by using an appropriately constructed sequence of Brillouin precursor pulses.