  We discuss the constraints coming from current observations of type Ia
supernovae on cosmological models which allow sudden future singularities of
pressure (with the scale factor and the energy density regular). We show that
such a sudden singularity may happen in the very near future (e.g. within ten
million years) and its prediction at the present moment of cosmic evolution
cannot be distinguished, with current observational data, from the prediction
given by the standard quintessence scenario of future evolution. Fortunately,
sudden future singularities are characterized by a momentary peak of infinite
tidal forces only; there is no geodesic incompletness which means that the
evolution of the universe may eventually be continued throughout until another
``more serious'' singularity such as Big-Crunch or Big-Rip.
