In 1980, David Bellamy constructed the first example of a tree-like continuum which does not have the fixed-point property. Several others have been constructed since, most recently in 2018 by Rodrigo Hern'{a}ndez-Guti'{e}rrez and Logan Hoehn. Their example is expressed as an inverse limit on trees, each of which is an arc with simple triods attached at select points. In this talk, I discuss the construction from Hern'{a}ndez-Guti'{e}rrez and Hoehn and give an overview of work towards a similar example where each factor space has branch points of lower degree. Joint work with Logan Hoehn.