A surface‐related multiple‐elimination method can be formulated as an iterative procedure: the output of one iteration step is used as input for the next iteration step (part I of this paper). In this paper (part II) it is shown that the procedure can be made very efficient if a good initial estimate of the multiple‐free data set can be provided in the first iteration, and in many situations, the Radon‐based multiple‐elimination method may provide such an estimate. It is also shown that for each iteration, the inverse source wavelet can be accurately estimated by a linear (least‐squares) inversion process. Optionally, source and detector variations and directivity effects can be included, although the examples are given without these options. The iterative multiple elimination process, together with the source wavelet estimation, are illustrated with numerical experiments as well as with field data examples. The results show that the surface‐related multiple‐elimination process is very effective in time gates where the moveout properties of primaries and multiples are very similar (generally deep data), as well as for situations with a complex multiple‐generating system.