Homeostatic processes that provide negative feedback to regulate neuronal firing rate are essential for normal brain function, and observations suggest that multiple such processes may operate simultaneously in the same network. We pose two questions: why might a diversity of homeostatic pathways be necessary, and how can they operate in concert without opposing and undermining each other? To address these questions, we perform a computational and analytical study of cell-intrinsic homeostasis and synaptic homeostasis in single-neuron and recurrent circuit models. We demonstrate analytically and in simulation that when two such mechanisms are controlled on a long time scale by firing rate via simple and general feedback rules, they can robustly operate in tandem to tune the mean and variance of single neuron's firing rate to desired goals. This property allows the system to recover desired behavior after chronic changes in input statistics. We illustrate the power of this homeostatic tuning scheme by using it to regain high mutual information between neuronal input and output after major changes in input statistics. We then show that such dual homeostasis can be applied to tune the behavior of a neural integrator, a system that is notoriously sensitive to variation in parameters. These results are robust to variation in goals and model parameters. We argue that a set of homeostatic processes that appear to redundantly regulate mean firing rate may work together to control firing rate mean and variance and thus maintain performance in a parameter-sensitive task such as integration.