The full reference tissue model (FRTM) is a PET analysis framework that includes both free and specifically bound compartments within tissues, together with rate constants defining association and dissociation from the specifically bound compartment. The simplified reference tissue model (SRTM) assumes instantaneous exchange between tissue compartments, and this "1-tissue" approximation reduces the number of parameters and enables more robust mapping of non-displaceable binding potentials. Simulations based upon FRTM have shown that SRTM exhibits biases that are spatially dependent, because biases depend upon binding potentials. In this work, we describe a regularized model (rFRTM) that employs a global estimate of the dissociation rate constant from the specifically bound compartment (k4). The model provides an internal calibration for optimizing k4 through the reference-region outflow rate k2', a model parameter that should be a global constant but varies regionally in SRTM. Estimates of k4 by rFRTM are presented for four PET radioligands. We show that SRTM introduces bias in parameter estimates by assuming an infinite value for k4, and that rFRTM ameliorates bias with an appropriate choice of k4. Theoretical considerations and simulations demonstrate that rFRTM reduces bias in non-displaceable binding potentials. A two-parameter reduction of the model (rFRTM2) provides robust mapping at a voxel-wise level. With a structure similar to SRTM, the model is easily implemented and can be applied as a PET reference region analysis that reduces parameter bias without substantially altering parameter variance.