The low-temperature magnetic structure of Ho has been studied using a combination of neutron-scattering and mean-field calculations. Re-examination of the cone and one-spin-slip phases has shown that the structures are distorted by interactions of trigonal symmetry, similar to those recently hypothesized for Er. In the cone phase below 18.5 K the moments have two out-of-plane tilt angles with a difference in angle of approximately 1.0\ifmmode^\circ\else\textdegree\fi{} about a mean value of 9.0\ifmmode^\circ\else\textdegree\fi{}. The spin-slip phases are more complex. The moments are modulated with a period twice that of the basic spin-slip structure, giving rise to additional peaks in the scattering. Spin-slip structures found in a c-axis field are shown to be consistent with our model. In zero field, the phase transition to the cone phase occurs in two distinct steps, as suggested by anomalies found in several bulk measurements. The intermediate phase has the wave vector locked into (1/6)${\mathbf{c}}^{\mathrm{*}}$, where any group of four moments has two tilted in one sense along c, and the other two adopt an equal and opposite tilt, resulting in no net c-axis moment. Below 18.5 K this arrangement then tilts out of the basal plane, forming the distorted cone structure.