We present a detailed structure function analysis of the UV variability of Q0957+561. From optical observations in the 2005−2007 seasons, we constructed normalized structure functions of the quasar luminosity at restframe wavelengths λ ∼ 2100 Å and λ ∼ 2600 Å. Old optical records (1995−1996 seasons) also allow the structure function to be obtained at λ ∼ 2100 Å, but 10 years ago in the observer's frame. These three structure functions are then compared to predictions of both simple and relatively sophisticated (incorporating two independent variable components) Poissonian models. We do not find clear evidence of a chromatic mechanism of variability. From the recent data, ∼100-d time-symmetric and ∼170-d time-asymmetric flares are produced at both restframe wavelengths. Taking into account measurements of time delays and the existence of an EUV/radio jet, reverberation is probably the main mechanism of variability. Thus, two types of EUV/X-ray fluctuations would be generated within or close to the jet and later reprocessed by the disc gas in the two emission rings, at λ ∼ 2100 Å and λ ∼ 2600 Å. The ∼100-d time-symmetric shots are also responsible for most of the ∼2100 Å variability detected in the old experiment (10 years ago). However, there is no evidence of asymmetric shots in the old UV variability. If reverberation is the involved mechanism of variability, this could mean an intermittent production of high-energy asymmetric fluctuations. The old records are also consistent with the presence of very short-lifetime (∼10 d) symmetric flares, which may represent additional evidence of time evolution. Despite these exciting findings, we cannot rule out the possibility of unfortunate gaps in the old light curves (or a relatively short monitoring period) and very short-timescale systematic noise. We also discuss the quasar structure that emerges from the variability scenario.