Maximum a posteriori (MAP) reconstruction makes use of an anatomical prior from CT or MRI imaging to enforce smoothness of reconstructed PET images while preserving anatomical edges. The tendency of this technique to smooth parts of the image between anatomical boundaries may reduce the detectability of functional lesions if, as is commonly the case, the edges of these lesions do not conform to anatomical boundaries. We have investigated the use of a functional prior in addition to an anatomical prior to improve the detection and quantification of lesions in PET imaging. We introduce a new parameter, Q, which controls the weight, β, of the functional prior on a spatially-variant basis, to enable a reduction of the smoothing effect in regions containing lesions. Such regions constitute the functional prior. They can be defined, for example, by applying a threshold to a preliminary reconstructed PET image. They are quarantined from the smoothing of the standard MAP algorithm, and subjected to a lesser degree of smoothing as determined by the combined effects of Q and β. We call this dual-prior technique quarantine MAP reconstruction (QMAP). Thus the method alters the degree of smoothing in specific parts of the image with the aim of enhancing lesion detectability. We have compared the QMAP algorithm in computer simulations with standard One-Step-Late (OSL) MAP reconstruction and OSL-MAP with CT prior information. QMAP provided better lesion contrast than the other algorithms, without altering the properties of other parts of the image.