The problem of estimating parameters of inspiraling compact binaries in the context of LISA has been addressed by a few authors in the past. But these initial works obtained the estimates assuming the LISA design sensitivity as a given. We have now extended these studies in the following ways [<a href=''http://arxiv.org/abs/gr-qc/0407008''>Rogan:2004wq</a>]. First, our estimation is performed not on idealized Michelson signals but on the 3 pseudo-detector strains obtained after effecting second generation TDI. Second, we do not ignore the effect of Doppler shifting of frequencies owing to the relative motion of LISA with respect to the source, while also allowing for the Doppler phase modulation. Third, we have developed a code for computing the standard error in parameter estimates for any set of source parameter values, such as the sky-position or the source frequency. Fourth, inaccurate signal modeling can lead to errors in parameter estimates at first order. Although this is not a worry for small mass binaries, nevertheless it can have a non-negligible effect, e.g., on the sky-position determination of extreme-mass-ratio-inspirals (EMRIs) (and, therefore, in doing cosmology with such objects). This still leaves us with the problem of LISA's source-confusion noise. A partial solution is discussed at the end of Sec. II.3.