Design space exploration during conceptual design is an active research field. Most approaches generate a number of feasible design points (complying with the constraints) and apply graphical post-processing to visualize correlations between variables, the Pareto frontier or a preference structure among the design solutions. The generation of feasible design points is often a statistical (Monte Carlo) generation of potential candidates sampled within initial variable domains, followed by a verification of constraint satisfaction, which may become inefficient if the design problem is highly constrained since a majority of candidates that are generated do not belong to the (small) feasible solution space. In this paper, we propose to perform a preliminary analysis with Constraint Programming techniques that are based on interval arithmetic to dramatically prune the solution space before using statistical (Monte Carlo) methods to generate candidates in the design space. This method requires that the constraints are expressed in an analytical form. A case study involving truss design under uncertainty is presented to demonstrate that the computation time for generating a given number of feasible design points is greatly improved using the proposed method. The integration of both techniques provides a flexible mechanism to take successive design refinements into account within a dynamic process of design under uncertainty.