In this paper we present the results of a short-term optical monitoring program of 13 blazars. The objects were monitored mostly in the R band for a total of ∼160 h between 2006 and 2011. We study the nature of the short-term variations and show that most of them could be described as slow, smooth and (almost) linear changes of up to ∼0.1 mag h−1, but that many objects show no short-term variations at all. In fact, we found only a ∼2 per cent chance of observing variability of more than 0.1 mag h−1 for the sample we observed. Hints of quasi-periodic oscillations at very low-amplitude levels are also found for some objects. We briefly discuss some of the possible mechanisms for generating the intra-night variability and the quasi-periodic oscillations.