Mobile offloading overcomes the resource limitations of offloader devices by splitting resource-intensive tasks and allocating subtasks to nearby offloadee devices. In processing its subtask, each offloadee effectively executes foreign and untrusted code which might both harm the device and exhaust its resources. Given the personal nature and constrained resources of offloadee devices, such as smartphones, precise control at the offloadee over the execution environment of offloaded tasks as well as the provided and consumed resources then is a natural requirement for the success of offloading approaches. We thus contribute a mechanism for fine-grained resource control of local task execution, benefitting allocation approaches by precisely assessing, advertising, and guaranteeing offloadee processing resources. Our design protects local device integrity and usability by isolating the execution of each task in a dedicated Linux container with precisely defined resource constraints. We highlight the performance and immediate applicability of our design through a prototypical implementation using LXC containers on COTS Android smartphones that achieves controllable task execution at minimal costs: Each container starts up in only 2 ms, imposes less than 5 % computation overhead, and consumes only 10MB of memory.