We expand our Bayesian Monte Carlo method for analyzing the light curves of gravitationally lensed quasars to simultaneously estimate time delays and the sizes of quasar continuum emission regions including their mutual uncertainties. We apply the method to HE1104-1805 and QJ0158-4325, two doubly imaged quasars with micro-lensing and intrinsic variability on comparable timescales. For HE1104-1805 the resulting time delay of Δt_(AB) = t_A - t_B = 162.2_(-5.9)~(+6.3) days and accretion disk size estimate of log {(r_s/cm)[cos (i)/0.5]~(1/2)} = 15.7_(-0.5)~(0.4) at 0.2 μm in the rest frame and for inclination i 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)[cos (i)/0.5]_(1/2)} = 14.9 ± 0.3 at 0.3 μm in the rest frame.
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