We present the results of the study of visible (UBVRIZ) intra-night microvariability in the blazar OJ 287. Useful observations (at least four integrations in a single band in a single night with a single telescope) were carried out on a total of 26 nights from November 1993 to November 1994. Relative photometry was taken against star 4, 10 and 11 of the standard sequence, principally in the Johnson V filter, using 82cm, 1m and 2.56m telescopes in Tenerife and La Palma. Globally, 73% of the nights show microvariability. We find strong indications of an anticorrelation of the amplitude of variability with the brightness of OJ 287 for quiescent activity. The lesser quantitites of data in other bands limit our ability to differentiate clearly between different models for the generation of microvariability. Our observations suggest though that at least three different mechanisms may be responsible for the observed characteristics of the light curve at different epochs.