We expand our Bayesian Monte Carlo method for analyzing the light curves of gravitationally lensed quasars to simultaneously estimate time delays and quasar structure including their mutual uncertainties. We apply the method to HE1104-1805 and QJ0158-4325, two doubly-imaged quasars with microlensing and intrinsic variability on comparable time scales. For HE1104-1805 the resulting time delay of (Delta t_AB) = t_A - t_B = 162.2 -5.9/+6.3 days and accretion disk size estimate of log(r_s/cm) = 15.7 -0.5/+0.4 at 0.2 micron in the rest frame are consistent with earlier estimates but suggest that existing methods for estimating time delays in the presence of microlensing underestimate the uncertainties. We are unable to measure a time delay for QJ0158-4325, but the accretion disk size is log(r_s/cm) = 14.9 +/- 0.3 at 0.3 micron in the rest frame.
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