Aims: The nature of Cygnus X-3 is still not understood well. This binary system might host a black hole or a neutron star. Recent observations by INTEGRAL have shown that Cygnus X-3 was again in an extremely ultrasoft state. Here we present our analysis of the transition from the ultrasoft state, dominated by blackbody radiation at soft X-rays plus non-thermal emission in the hard X-rays, to the low hard state. Methods: INTEGRAL observed Cyg X-3 six times during three weeks in late May and early June 2007. Data from IBIS/ISGRI and JEM-X1 were analysed to show the spectral transition. Results: During the ultrasoft state, the soft X-ray spectrum is well-described by an absorbed (NH = 1.5E22 1/cm**2) black body model, whereas the X-ray spectrum above 20 keV appears to be extremely low and hard (Gamma = 1.7). During the transition, the radio flux rises to a level of >1 Jy, and the soft X-ray emission drops by a factor of 3, while the hard X-ray emission rises by a factor of 14 and becomes steeper (up to Gamma = 4). Conclusions: The ultrasoft state apparently precedes the emission of a jet, which is apparent in the radio and hard X-ray domain. Comment: 4 pages, 3 figures, accepted for publication as A&A Research Note