Traits that have arisen multiple times yet still remain rare present a curious paradox. A number of these rare traits show a distinct tippy pattern, where they appear widely dispersed across a phylogeny, are associated with short branches and differ between recently diverged sister species. This phylogenetic pattern has classically been attributed to the trait being an evolutionary dead end, where the trait arises due to some short‐term evolutionary advantage, but it ultimately leads species to extinction. While the higher extinction rate associated with a dead end trait could produce such a tippy pattern, a similar pattern could appear if lineages with the trait speciated slower than other lineages, or if the trait was lost more often that it was gained. In this study, we quantify the degree of tippiness of red flowers in the tomato family, Solanaceae, and investigate the macroevolutionary processes that could explain the sparse phylogenetic distribution of this trait. Using a suite of metrics, we confirm that red‐flowered lineages are significantly overdispersed across the tree and form smaller clades than expected under a null model. Next, we fit 22 alternative models using HiSSE (Hidden State Speciation and Extinction), which accommodates asymmetries in speciation, extinction and transition rates that depend on observed and unobserved (hidden) character states. Results of the model fitting indicated significant variation in diversification rates across the family, which is best explained by the inclusion of hidden states. Our best fitting model differs between the maximum clade credibility tree and when incorporating phylogenetic uncertainty, suggesting that the extreme tippiness and rarity of red Solanaceae flowers makes it difficult to distinguish among different underlying processes. However, both of the best models strongly support a bias towards the loss of red flowers. The best fitting HiSSE model when incorporating phylogenetic uncertainty lends some support to the hypothesis that lineages with red flowers exhibit reduced diversification rates due to elevated extinction rates. Future studies employing simulations or targeting population‐level processes may allow us to determine whether red flowers in Solanaceae or other angiosperms clades are rare and tippy due to a combination of processes, or asymmetrical transitions alone.