We outline a model of abelian-Higgs strings with variable scalar and vector core radii. In general, the functions determining the time and position-dependent core widths may be expressed as arbitrary left or right movers, of which the usual constant values are a particular solution. In this case the string may carry momentum, even if the embedding of its central axis remains fixed, and the resulting objects resemble "necklaces". Some possible astrophysical applications of lumpy strings, including as potential engines for anomalous gamma ray bursts, are also discussed.