We study the conductance threshold of clean nearly straight quantum wires in which an electron is bound. We show that such a system exhibits spin-dependent conductance structures on the rising edge to the first conductance plateau; one near 0.25(2e ² /h ), related to a singlet resonance, and one near 0.75(2e ² /h ), related to a triplet resonance. As a quantitative example we solve exactly the scattering problem for two-electrons in a wire with planar geometry and a weak bulge. From the scattering matrix we determine conductance via the Landauer-Büttiker formalism. The conductance anomalies are robust and survive to temperatures of a few degrees. With increasing in-plane magnetic field the conductance exhibits a plateau at e ² /h , consistent with recent experiments.