The continuous double-auction (CDA) is a powerful market mechanism, noted for its speed and efficiency, and is the mechanism underlying the organization of open-outcry 'trading pits' at major international derivatives markets. In previous publications, Cliff & Bruten demonstrated that software 'trading agents' need more than zero intelligence to give human-like CDA price-equilibration behavior and presented results from experiments with simple adaptive trading agents in CDA markets and in one-sided auctions. These agents give very good performance on standard measures of trading activity such as allocative efficiency, Smith's 'alpha' measure of price convergence, and profit dispersion, but only when parameters governing the adaptation mechanism are set to appropriate values. Determining good or optimal combinations of parameters by hand is possible, but can be labor- intensive. This paper presents the first results from using a genetic algorithm to optimize all the real- valued parameters governing adaptation in the trading agents. It is shown that a simple genetic algorithm (GA), in combination with an appropriate evaluation function, can deliver good parameter settings from random initial-value conditions. The evolutionary trajectories of the population through the 8- dimensional parameter space are illustrated, and the use of the GA to identify parameters that are redundant or even harmful is discussed. 23 Pages