Eukaryotic cells, including some human cancers, that lack telomerase can sometimes maintain telomeres by using recombination. It was recently proposed that recombinational telomere elongation (RTE) in a telomerase-deletion mutant of the yeast Kluyveromyces lactis occurs through a roll-and-spread mechanism as described in our previous work. According to this model, a tiny circle of telomeric DNA is copied by a rolling-circle mechanism to generate one long telomere, the sequence of which is then spread to all other telomeres by gene-conversion events. In support of this model, we demonstrate here that RTE in K. lactis occurs by amplification of a sequence originating from a single telomere. When a mutationally tagged telomere is of normal length, its sequence is spread to all other telomeres at a frequency (approximately 10%) consistent with random selection among the 12 telomeres in the cell. However, when the mutationally tagged telomere is considerably longer than other telomeres, cellular senescence is partially suppressed, and the sequence of the tagged telomere is spread to all other telomeres in >90% of cells. Strikingly, the transition between a state resistant to recombination and a state capable of initiating recombination is abrupt, typically occurring when telomeres are approximately 3-4 repeats long. Last, we show that mutant repeats that are defective at regulating telomerase are also defective at regulating telomere length during RTE.