Characterisation of the T cell receptors (TCR) involved in immune responses is important for the design of vaccines and immunotherapies for cancer and autoimmune disease. The specificity of the interaction between the TCR heterodimer and its peptide-MHC ligand derives largely from the juxtaposed hypervariable CDR3 regions on the TCRα and TCRβ chains, and obtaining the paired sequences of these regions is a standard for functionally defining the TCR. A brute force approach to identifying the TCRs in a population of T cells is to use high-throughput single-cell sequencing, but currently this process remains costly and risks missing small clones. Alternatively, CDR3α and CDR3β sequences can be associated using their frequency of co-occurrence in independent samples, but this approach can be confounded by the sharing of CDR3α and CDR3β across clones, commonly observed within epitope-specific T cell populations. The accurate, exhaustive, and economical recovery of TCR sequences from such populations therefore remains a challenging problem. Here we describe an algorithm for performing frequency-based pairing (alphabetr) that accommodates CDR3α- and CDR3β-sharing, cells expressing two TCRα chains, and multiple forms of sequencing error. The algorithm also yields accurate estimates of clonal frequencies.