Some aspects of the variation of the alpha-particle abundance in the solar wind are studied using Ulysses data. We focus on the first mid-latitude phase of the mission, when the spacecraft intermittently enters the fast high-latitude wind, and on the region around the first perihelion passage, when low-latitude wind in conditions of low solar activity is observed. In particular, we look for the existence of a relationship between the alpha-particle abundance and the solar wind velocity. No evidence of correlation is found for the midlatitude wind, while at low latitudes a positive correlation emerges. This difference may be indicative of a different relevance, in the two regions, of the processes that can be at the origin of low-speed solar wind. At mid latitudes the low velocity of the wind would be mainly due to the topology of the solar magnetic field, with a large expansion factor. Near the equator this effect would become weaker and a dominant role would be played by source region features related to the alpha-particle content.