[en] In a computerized adaptive test (CAT), we seek an acceptably accurate trait (θ) level estimate using an optimal number of items. Bayesian estimation methods like MAP and EAP are often used to compute that estimate. Unfortunately, with such methods, decreasing the number of items generates bias whenever the true θ level differs significantly from the a priori estimate. Adaptive versions of the maximum a posteriori and expected a posteriori estimation methods are proposed to reduce this bias. These AMAP and AEAP methods adapt the a priori values used in the estimation function according to the previously computed θ estimate obtained from the previous administered item. The performance of AMAP and AEAP is evaluated in a CAT context.