The function of yeast Rap1 as an activator in transcription, a repressor at silencer elements, and as a major component of the shelterin-like complex at telomeres requires the known high-affinity and specific interaction of the DNA-binding domain (DBD) with its recognition sequences. In addition to a high-affinity one-to-one complex with its DNA recognition site, Rap1(DBD) also forms lower affinity complexes with higher stoichiometries on DNA. We proposed that this originates from the ability of Rap1(DBD) to access at least two DNA-binding modes. In this work, we show that Rap1(DBD) binds in multiple binding modes to recognition sequences that contain different spacer lengths between the hemi-sites. We also provide evidence that in the singly-ligated complex Rap1(DBD) binds quite differently to these sequences. Rap1(DBD) also binds to a single half-site but does so using the alternative DNA-binding mode where only a single Myb-like domain interacts with DNA. We found that all arrangements of Rap1 sites tested are represented within the telomeric sequence and our data suggest that at telomeres Rap1 might form a nucleoprotein complex with a heterogeneous distribution of bound states.