The invention is directed to sequence-based profiling of populations of nucleic acids by multiplex amplification and attachment of one or more sequence tags to target nucleic acids and/or copies thereof followed by high-throughput sequencing of the amplification product. In some embodiments, the invention includes successive steps of primer extension, removal of unextended primers and addition of new primers either for amplification (for example by PCR) or for additional primer extensions. Some embodiments of the invention are directed to minimal residual disease (MRD) analysis of patients being treated for cancer. Sequence tags incorporated into sequence reads provide an efficient means for determining clonotypes and at the same time provide a convenient means for detecting carry-over contamination from other samples of the same patient or from samples of a different patient which were tested in the same laboratory.