Heiða has performed extensively in Iceland, Holland, Belgium and France in modes varying from Church music to lied- and modern music. She has been very active in the modern music scene in Iceland and has frequently performed with the ensemble Adapter. Her biggest passion, however, is singing with her group, the quartet Mógil which plays experimental folk jazz and has released two albums, ‘Ró’ (2008) and ‘Í stillunni hljmar’ (2011). Mógil composes their own songs, as accompaniments to ancient Icelandic folk texts. New lyrics are written in traditional styles. Critics have described these as ‘lyrical and sweet’, showing continuities with the traditional Icelandic Lied style. Mógil has played at many festivals e.g. WOMEX World festival, Reykjavík Jazz Festival and Iceland Airwaves and has toured several times around in Belgium, Holland, Denmark, Sweden and Iceland.