Improved computer-aided design tools can significantly impact designer productivity. The ability to formulate and solve "What if* questions is critical in early design stages. In this paper, a new computational framework for preliminary design, called Goal-Directed Geometry, is presented that provides such an exploratory environment for early stages. Tools for parametric geometry, variational modeling, and feature-based design are combined with a multiobjective optimization code to provide robust support for parametric design problems, where parameter values are desired that best meet a set of goals and constraints. Geometric and engineering models of a design are combined into a multiobjective optimization formulation called a Compromise Decision Support Problem, which can be solved by the existing package DSIDES (Decision Support In the Design of Engineering Systems). A prototype CAD system is under development that integrates DSIDES, a geometric modeler, and variational, parametric, and feature capabilities. The system aids a designer in evaluating competing alternatives, common during preliminary design, and in answering "What if' types of questions. Two examples illustrate the use of Goal-Directed Geometry in formulating and solving parametric design problems involving engineering and geometric constraints and goals.