The magnetic structure and energy dissipation at low-Mach-number, quasi-parallel collisionless shocks are examined through observations obtained by the ISEE 1 and 2 spacecraft at seven crossings of the Earth's dayside bow shock. The Alfv¿n Mach number of the shocks in this set ranges from 2.0 to 3.7, and the angle &thgr;Bn between the shock normal and the average upstream magnetic field direction ranges from 2¿ to 39¿ The shocks all exhibit a fairly short-scale-length ramp where the principal jumps in the electron temperature, ion temperature, and magnetic field strength take place. Large-amplitude, low-frequency, transverse waves in the magnetic field are present in and downstream from the ramp, with more modest waves upstream. The amplitude of the downstream waves is typically larger than can be accounted for by shock compression of the upstream waves. The electron heating represents about 6% of the dissipated bulk flow energy, consistent with observations in other parameters regimes, and suggesting that the dominant electron heating process is the same. The electron share of the dissipated energy appears to increase somewhate with increasing &thgr;Bn, and the ion share appears to decrease. Coherent reflection of incident ions does not appear to be very important for ion heating at these low Mach numbers, although a low level of reflection may contribute significantly to the generation of the large-amplitude waves. Finally, the downstream ion distributions do not show the strong variability previously interpreted as evidence for a cyclic re-formation process at higher-Mach-number, quasi-parallel shocks. It is possible that the low-Mach-number shocks are re-forming but do no exhibit the downstream variability because of the relatively low levels of reflected ions.