Telomerase is a specialized reverse transcriptase that contains an integral RNA subunit including a short template sequence. It extends telomeric 3′ overhangs and chromosome breakpoints by catalyzing reiterative copying of this internal template into single-stranded telomeric DNA repeats. Here we report for the first time that in vitro the ciliate Tetrahymena telomerase can efficiently extend very short single-stranded DNA primers (<6 nt). These data indicate that interactions with nucleotides further upstream are not essential for elongation of longer primers. We also report that the minimal lengths required for primers to be extended by the telomerase depend on the positions along the template at which the primers are initially aligned. At a primer concentration of 2.5 µM, primers aligned in the beginning, middle and next to the end of the template, respectively, must consist of at least 4, 5 and 6 nt to be extended by the telomerase. At a primer concentration of 50 µM, the corresponding minimal lengths are 3, 4 and 5 nt. The systematic variation of the minimal required primer lengths supports the presence of a site within the telomerase ribonucleoprotein complex that mediates specific positioning of 3′ termini of telomeric and non-telomeric DNA in the beginning of the template during telomere synthesis.