DNA intercalators are widely used as fluorescent probes to visualize DNA and DNA transactions in vivo and in vitro. It is well known that they perturb DNA structure and stability, which can in turn influence DNA-processing by proteins. Here we elucidate this perturbation by combining single-dye fluorescence microscopy with force spectroscopy and measuring the kinetics of DNA intercalation by the mono- and bis-intercalating cyanine dyes SYTOX Orange, SYTOX Green, SYBR Gold, YO-PRO-1, YOYO-1 and POPO-3. We show that their DNA-binding affinity is mainly governed by a strongly tension-dependent dissociation rate. These rates can be tuned over a range of seven orders of magnitude by changing DNA tension, intercalating species and ionic strength. We show that optimizing these rates minimizes the impact of intercalators on strand separation and enzymatic activity. These new insights provide handles for the improved use of intercalators as DNA probes with minimal perturbation and maximal efficacy.