ABSTRACT Co-moving groups of stars (streams) are well known in the velocity space of the disc near the Sun. Many are thought to arise from resonances with the Galactic bar or spiral arms. In this work, we search for similar moving groups in the velocity space of the halo, at low angular momentum. From the asymmetry of the radial velocity distribution $v_\mathrm{ R}$, we identify two inward-moving streams with $v_\mathrm{ R}< 0$ and small $|v_\phi |$. These are projections of the ‘chevrons’ previously discovered in radial phase space $(R,v_\mathrm{ R})$. A test particle simulation in a realistic Milky Way potential with a decelerating bar naturally produces analogues of these features, and they are observed across a wide range of metallicity. They are therefore very likely to be dynamical streams created by trapping in the bar’s resonances. Specifically, they occupy regions of phase space where orbits are trapped in the corotation and outer Lindblad resonances respectively. By tracing these streams across a range of radii in $(R,v_\mathrm{ R})$ space, we fit resonant orbits to their tracks in a flexible potential with variable bar pattern speed. This allows us to simultaneously constrain the mass profile of the Milky Way for $r\lesssim 20$ kpc and the pattern speed $\Omega _\mathrm{b}$. We estimate the mass enclosed within $r=20$ kpc to be $M_{20}=(2.17\pm 0.21)\times 10^{11}\,\mathrm{ M}_\odot$, and the pattern speed to be $\Omega _\mathrm{b}=31.9_{-1.9}^{+1.8}$ km s−1 kpc−1. Our fitted potential is in excellent agreement with previous results, while we favour a slightly slower pattern speed than most recent estimates.