This paper presents an approach to solving constraint satisfaction problems using Asynchronous Teams of autonomous agents (ATeams). The focus for the constraint satisfaction problem is derived from an effort to support spatial layout generation in a conceptual design framework. The constraint specification allows a high-level representation and manipulation of qualitative geometric information. We present a computational technique based on ATeams to instantiate solutions to the constraint satisfaction problem. The technique uses a search for a solution in numerical space. This permits us to handle both qualitative relationships and numerical constraints in a unified framework. We show that simple knowledge, about human spatial reasoning and about the nature of arithmetic operators can be hierarchically encapsulated and exploited efficiently in the search. An example illustrates the generality of the approach for conceptual design. We also present empirical studies that contrast the efficiency of ATeams with a search based on genetic algorithms. Based on these preliminary results, we argue that the ATeams approach elegantly handles arbitrary sets of constraints, is computationally efficient, and hence merits further investigation.