Existing models decomposing the bid-ask spread into three components (adverse selection, inventory holding and order-processing) do not in many cases give sensible results. This paper suggests a new quote-based model for decomposing the bid-ask spread into three components, and uses it to explore a number of interesting issues. First, we examine intra-daily behavior of the components for actively traded stocks. Second, we investigate the impact of decimalization on the spread and its components. Finally, we contribute to the debate on how trading systems affect the spread and its sources. Some of the results we obtain are new, some are richer and broader, while others are qualitatively the same as in the previous literature.