This paper investigates the maximization of the secrecyachievable rate region for the Gaussian broadcast channel with confidential message (BCCM) using finite input constellations. The maximization is done jointly over symbol positions and their joint probabilities. The secrecy-achievable rate regions are given for various broadcast strategies which differ in their complexity of implementation. We compare these strategies in terms of improvement in achievable rates and we study the impact of finite input alphabet on the secrecyachievable rates. It is shown that finite alphabet constraints may change well known results holding in the Gaussian case.