We present a case study of grammatical tone allomorphy in Cilungu (Bantu). Tense/Aspect/Mood designations (TAMs) are realized via co-exponence of prefixes, suffixes, and floating tones. In a minority of TAMs, there is allomorphy with the floating tones. For example, in the Recent Past one allomorph involves floating tone targeting the final mora of the stem ("Equation missing") versus one targeting the stem’s second mora ("Equation missing"2). For all such allomorphic TAMs, the alternation is conditioned by the tone of subject agreement markers (SMs) at the left edge of the word. If the SM is high-toned the "Equation missing" variant occurs, but if it is toneless then "Equation missing"2 occurs. We present two competing accounts of these data. Under a morphological account, we posit contextual realizational rules with multiple suppletive exponents conditioned by SM tone. In contrast, under a phonological account a ‘first-last tone harmony’ applies here, morphologically restricted to the context of SMs with a small set of TAMs. Such a harmony rule captures a generalization of these alternations: if the SM is high at the left edge then there is a grammatical high at the right edge, but if the left edge is toneless then grammatical tone does not fall on the right edge. We present several arguments in favor of the morphological analysis (suppletion) over a phonological one (harmony). Specifically, the patterns are not subject to phonological locality, other TAMs involving similar tone patterns are not subject to this harmony, and the proposed first-last tone harmony would be a highly phonologically-unnatural rule with little cross-linguistic support, and exceeding the computational properties of all well-known and established phonological operations. We conclude by discussing a major theoretical implication of the morphological account: this constitutes outward-sensitive phonologically-conditioned suppletive allomorphy, standardly argued to be unattested and/or impossible. Ultimately, we hold that under either account Cilungu presents a novel and important contribution to linguistic theory.