Short, non-encoded oligo(A), oligo(U), or A/U tails can impact mRNA stability in kinetoplastid mitochondria. However, a comprehensive picture of the relative effects of these modifications in RNA stability is lacking. Furthermore, while the U-preferring exoribonuclease TbRND acts on U-tailed gRNAs, its role in decay of uridylated mRNAs has only been cursorily investigated. Here, we analyzed the roles of mRNA 3′ tail composition and TbRND in RNA decay using cells harbouring single or double knockdown of TbRND and the KPAP1 poly(A) polymerase. Analysis of mRNA abundance and tail composition reveals dramatic and transcript-specific effects of adenylation and uridylation on mitochondrial RNAs. Oligo(A) and A-rich tails can stabilize a proportion of edited and never-edited RNAs. However, non-tailed RNAs are not inherently unstable, implicating additional stability determinants and/or spatial segregation of sub-populations of a given RNA in regulation of RNA decay. Oligo(U) tails, which have been shown to contribute to decay of some never-edited RNAs, are not universally destabilizing. We also show that RNAs display very different susceptibility to uridylation in the absence of KPAP1, a factor that may contribute to regulation of decay. Finally, 3′ tail composition apparently impacts the ability of an RNA to be edited.