A vaccine containing a H1 subtype influenza A virus hemagglutinin is either unadjuvanted or is adjuvanted but not with an oil-in-water emulsion adjuvant. The vaccine is suitable for immunizing a patient against swine flu. The vaccine may be monovalent. The vaccine may include two different H1 subtype influenza A virus hemagglutinins, wherein (i) the first H1 subtype influenza A virus hemagglutinin is more closely related to SEQ ID NO: 1 than to SEQ ID NO: 3 and (ii) the second H1 subtype influenza A virus hemagglutinin is more closely related to SEQ ID NO: 3 than to SEQ ID NO: 1. A monovalent vaccine may be administered in conjunction with a trivalent A/H1N1-A/H3N2 B seasonal influenza vaccine. Other embodiments are also disclosed, such as reassortant viruses.