Interest in the transmission of high intensities through optical fibers is being motivated by an increasing number of applications. Using different laser types and fiber materials, various studies are encountering transmission limitations due to laser-induced damage processes. For a number of years we have been investigating these limiting processes during the transmission of Q-switched, multimode, Nd:YAG laser pulses through step-index, multimode, fused- silica fiber. We have found that fiber transmission is often limited by a plasma-forming breakdown occurring at the fiber entrance face. This breakdown can result in subtle surface modifications that leave the entrance face more resistant to further breakdown or damage events. Catastrophic fiber damage can also occur as a result of a variety of mechanisms, with damage appearing at fiber entrance and exit faces, within the initial 'entry' segment of the fiber path, and at other internal sites due to fiber fixturing and routing effects. System attributes that will affect breakdown and damage thresholds include laser characteristics, the design and alignment of laser-to-fiber injection optics, and fiber end-face preparation. In the present work we have combined insights gained in past studies in order to establish what thresholds can be achieved if all system attributes can be optimized to some degree. Our multimode laser utilized past modifications that produced a relatively smooth, quasi-Gaussian profile. The laser-to-fiber injection system achieved a relatively low value for the ratio of peak-to-average fluences at the fiber entrance face, incorporated a mode scrambler to generate a broad mode power distribution within the initial segment of the fiber path, and had improved fixturing to insure that the fiber axis was collinear with the incident laser beam. Test fibers were from a particular production lot for which initial-strength characteristics were established and a high-stress proof test was performed. Fiber end faces were prepared by a careful mechanical polishing schedule followed by surface conditioning using a CO2 laser. In combination, these factors resulted in higher thresholds for breakdown and damage than we had achieved previously in studies that utilized a simple lens injection system. Probability distribution functions were fitted to the threshold data, providing a means for estimating the probability for transmission failure at lower laser energies.