Maintaining telomeric DNA at chromosome ends is essential for genome stability. In virtually all organisms the telomerase enzyme provides this function; however, telomerase-independent mechanisms also exist. These latter mechanisms rely on recombination pathways to replenish telomeric DNA and extrachromosomal DNA may also be implicated. Here, we report that in Saccharomyces cerevisiae cells, extrachromosomal circular DNA occurs for both subtypes of telomerase-independent telomere-maintenance mechanisms. This DNA consists of circular molecules of full-length subtelomeric repeat elements in type I cells, and very heterogeneously sized circles of telomeric repeat DNA in type II cells that are at least partially single stranded. Surprisingly, both type I and type II cells can adapt to a loss of the normally essential telomere-capping protein Cdc13p by inducing an alternate and reversible state of chromosome ends. Chromosome capping, therefore, is not strictly dependent on canonical capping proteins, such as Cdc13p, but can be achieved by alternate mechanisms.