In this paper, we analyze the impact of leverage deviation (i.e., actual minus target optimal leverage) on the implied cost of equity capital. Our special focus is on whether (and to what extent) the sensitivity of the cost of equity to leverage deviation, influences the speed with which firms adjust their financial leverage toward the target. Confirming theoretical predictions, we find that the cost of equity is positively related to leverage deviation and that firms whose cost of equity is more sensitive to leverage deviation exhibit faster speed of adjustment toward the target. Collectively, our findings imply that capital structure targeting is not equally important to all firms. Indeed, we argue that while evidence of the trade-off theory will tend to be obscured in broad samples, it can hold strongly in meaningfully chosen sub-samples of firms - namely, those characterized by high sensitivity of equity cost to leverage deviation.