Large errors in the estimation of volume of distribution (Vd) for sparse data

Dear all, I have some population PK data which are in general very sparse (95% have only 1 blood sample between 2 successive doses). I developed a population PK model with the one-compartment model with 1st order absorption. The progress is generally okay except that whenever a random effect, i.e. *(1+ETA(1)), is used to describe distribution of Vd, OMEGA would be estimated to be very large (around 45% in terms of CV, with 80% Shrinkage), despite statistical significance (dOF approx. -5.5). So I dropped the random effect and expressed Vd in terms of a single fixed effect. When the final model has come out, I performed bootstrap and found that most estimates are accurate except Vd, which has a very large standard error and bias (mean 232, bias 49, SE 156), while the estimates for CL and other parameters look normal. I then constructed the predictive plots for the developed model using both the original estimates (i.e. estimates using my original dataset) (#1) and estimates from one of the bootstrap runs which has an extreme estimate of Vd (9xx) (#2), and found out that the two plots of plasma profiles are quite different in terms of the shape (#1 is "taller", #2 is much flatter) but have similar average Cp. These seem to be suggesting that given my sparse data, it is impossible to require accurate estimations of both CL and Vd. Apart from fixing Vd to a fixed value, is there any other possible solutions? Or is there anything that I might have overlooked? Thanks and regards, Matthew