Project managers are faced with the challenging task of managing an environment filled with uncertainties that may lead to multiple disruptions during project execution. In particular, they are frequently confronted with planning for routine and non-routine unplanned work: known, identified, tasks that may or may not occur depending upon various, often unpredictable, factors. This problem is known as the stochastic task insertion problem, where tasks of deterministic duration occur stochastically. Traditionally, project managers may include an extra margin within deterministic task times or an extra time buffer may be allotted at the end of the project schedule to protect the final project completion milestone. Little scientific guidance is available to better integrate buffers strategically into the project schedule. Motivated by the Critical Chain and Buffer Management approach of Goldratt, this research identifies, defines, and demonstrates new buffer sizing techniques to improve project duration and stability metrics associated with the stochastic resource constrained project scheduling problem with stochastic task insertions. Specifically, this research defines and compares partial buffer sizing strategies for projects with varying levels of resource and network complexity factors as well as the level and location of the stochastically occurring tasks. Several project metrics may be impacted by the stochastic occurrence or non-occurrence of a task such as the project makespan and the project stability. New duration and stability metrics are developed in this research and are used to evaluate the effectiveness of the proposed buffer sizing techniques. These "robustness measures" are computed through the comparison of the characteristics of the initial schedule (termed the infeasible base schedule), a modified base schedule (or as-run schedule) and an optimized version of the base schedule (or perfect knowledge schedule). Seven new buffer sizing techniques are introduced in this research. Three are based on a fixed percentage of task duration and the remaining four provide variable buffer sizes based upon the location of the stochastic task in the schedule and knowledge of the task stochasticity characteristic. Experimental analysis shows that partial buffering produces improvements in the project stability and duration metrics when compared to other baseline scheduling approaches. Three of the new partial buffering techniques produced improvements in project metrics. One of these partial buffers was based on a fixed percentage of task duration and the other two used a variable buffer size based on knowledge of the location of the task in the project network. This research provides project schedulers with new partial buffering techniques and recommendations for the type of partial buffering technique that should be utilized when project duration and stability performance improvements are desired. When a project scheduler can identify potential unplanned work and where it might occur, the use of these partial buffer techniques will yield a better estimated makespan. Furthermore, it will result in less disruption to the planned schedule and minimize the amount of time that specific tasks will have to move to accommodate the unplanned tasks.