We investigated evolutionary relationships among deuterostome subgroups by obtaining nearly complete large-subunit ribosomal RNA (LSU rRNA)-gene sequences for 14 deuterostomes and 3 protostomes and complete small-subunit (SSU) rRNA-gene sequences for five of these animals. With the addition of previously published sequences, we compared 28 taxa using three different data sets (LSU only, SSU only, and combined LSU + SSU) under minimum evolution (with LogDet distances), maximum likelihood, and maximum parsimony optimality criteria. Additionally, we analyzed the combined LSU + SSU sequences with spectral analysis of LogDet distances, a technique that measures the amount of support and conflict within the data for every possible grouping of taxa. Overall, we found that (1) the LSU genes produced a tree very similar to the SSU gene tree, (2) adding LSU to SSU sequences strengthened the bootstrap support for many groups above the SSU-only values (e.g., hemichordates plus echinoderms as Ambulacraria; lancelets as the sister group to vertebrates), (3) LSU sequences did not support SSU-based hypotheses of pterobranchs evolving from enteropneusts and thaliaceans evolving from ascidians, and (4) the combined LSU + SSU data are ambiguous about the monophyly of chordates. No tree-building algorithm united urochordates conclusively with other chordates, although spectral analysis did so, providing our only evidence for chordate monophyly. With spectral analysis, we also evaluated several major hypotheses of deuterostome phylogeny that were constructed from morphological, embryological, and paleontological evidence. Our rRNA-gene analysis refutes most of these hypotheses and thus advocates a rethinking of chordate and vertebrate origins.