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The blazar AO 0235+164 was claimed to show a quasi-periodic behaviour in the radio and optical bands. Moreover, an extra emission component contributing to the UV and soft X-ray flux was detected, whose nature is not yet clear. A predicted optical outburst was observed in late 2006/early 2007. We here present the radio-to-optical WEBT light curves during the outburst, together with UV data acquired by Swift in the same period. We found the optical outburst to be as strong as the big outbursts of the past: starting from late September 2006, a brightness increase of 5 mag led to the outburst peak in February 19-21, 2007. We also observed an outburst at mm and then at cm wavelengths, with an increasing time delay going toward lower frequencies during the rising phase. Cross-correlation analysis indicates that the 1 mm and 37 GHz flux variations lagged behind the R-band ones by about 3 weeks and 2 months, respectively. These short time delays suggest that the corresponding jet emitting regions are only slightly separated and/or misaligned. In contrast, during the outburst decreasing phase the flux faded contemporaneously at all cm wavelengths. This abrupt change in the emission behaviour may suggest the presence of some shutdown mechanism of intrinsic or geometric nature. The behaviour of the UV flux closely follows the optical and near-IR one. By separating the synchrotron and extra component contributions to the UV flux, we found that they correlate, which suggests that the two emissions have a common origin., Comment: 9 pages, 7 figures, in press for Astronomy and Astrophysics