We analyse the components of the bid-ask spread in the Athens Stock Exchange (ASE), which was recently characterised as a developed market. For large and medium capitalisation stocks, we estimate the adverse selection and the order handling component of the spreads as well as the probability of a trade continuation on the same side of either the bid or the ask price, using the Madhavan et al. (1997)model. We extend it by incorporating the traded volume and we find that the adverse selection component exhibits U-shape patterns, while the cost component pattern depends on the stock price. For high priced stocks, the usual U-shape applies, while for low-priced ones, it is an increasing function of time, mainly due to the order handling spread component. Furthermore, the expected price change and the liquidity adjustment to Value-at-Risk that is needed are higher in the low capitalisation stocks, while the most liquid stocks are the high priced ones. Moreover, by estimating the Madhavan et al. (1997)model for two distinct periods we explain why there are differences in the components of the bid-ask spread.