Chemotaxis, the directed motion of cells in response to chemical gradients, is important for a variety of biological processes ranging from embryogenesis to killing of pathogens. Increasing the speed and efficiency of directed migration is critical in such situations. We provide a control mechanism by which one can minimize the noise-driven firings at the back of the cell, enabling faster motion towards the front. We achieve this through a mechanism called absolute concentration robustness (ACR), which robustly maintains the steady-state concentration of intracellular biochemical species and, at the same time, provides control over the concentration variance. More particularly, by incorporating ACR, we develop a correspondence between the concentration mean and variance - both of which are independent of total concentrations. We show that by incorporating ACR into the back of a moving cell, we can create a mechanism to robustly control the noise variance at the back - thus limiting the deterring firings while the cell moves in the direction of the gradient.