We have integrated the orbits of 27,700 test particles initially entering the planetary system from the Oort cloud in order to study the origin of Halley-type comets (HTCs). We included the gravitational influence of the Sun, giant planets, passing stars, and Galactic tides. We find that an isotropically distributed Oort cloud does not reproduce the observed orbital element distribution of the HTCs. In order to match the observations, the initial inclination distribution of the progenitors of the HTCs must be similar to the observed HTC inclination distribution. We can match the observations with an Oort cloud that consists of an isotropic outer cloud and a disklike massive inner cloud. These idealized two-component models have inner disks with median inclinations that range from 10° to 50°. This analysis represents the first link between observations and the structure of the inner Oort cloud.