Ultra-short-pulse reflectometry is studied by means of the numerical integration of a one-dimensional full-wave equation for ordinary modes propagating in a plasma. The numerical calculations illustrate the potential of using the reflection of ultra-short-pulse microwaves as an effective probe of the density profile even in the presence of density fluctuations in a plasma. The difference in time delays of differing frequency components of the microwaves can be used to deduce the density profile. The modification of the reflected pulses in the presence of density fluctuations is examined and can be understood based on considerations of Bragg resonance. A simple and effective profile-reconstruction algorithm using the zero-crossings of the reflected pulse and subsequent Abel inversion is demonstrated. The robustness of the profile reconstruction algorithm in the presence of a sufficiently small-amplitude density perturbation is assessed. The reconstruction algorithm begins to fail when the scaled density perturbation is large enough to invalidate the first Born approximation description of scattering by density fluctuations.