The blazar 3C 454.3 underwent an unprecedented optical outburst in spring 2005. This was first followed by a mm and then by a cm radio outburst, which peaked in February 2006. We report on follow-up observations by the WEBT to study the multiwavelength emission in the post-outburst phase. XMM-Newton observations on July and December 2006 added information on the X-ray and UV fluxes. The source was in a faint state. The radio flux at the higher frequencies showed a fast decreasing trend, which represents the tail of the big radio outburst. It was followed by a quiescent state, common at all radio frequencies. In contrast, moderate activity characterized the NIR and optical light curves, with a progressive increase of the variability amplitude with increasing wavelength. We ascribe this redder-when-brighter behaviour to the presence of a little blue bump due to line emission from the broad line region, which is clearly visible in the source SED during faint states. Moreover, the data from the XMM-Newton OM reveal a rise of the SED in the UV, suggesting the existence of a big blue bump due to thermal emission from the accretion disc. The X-ray spectra are well fitted with a power-law model with photoelectric absorption, possibly larger than the Galactic one. However, the comparison with previous X-ray observations would imply that the amount of absorbing matter is variable. Alternatively, the intrinsic X-ray spectrum presents a curvature, which may depend on the X-ray brightness. In this case, two scenarios are possible.
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