  We discuss combined constraints, coming from the cosmic microwave background
shift parameter $\mathcal{R}$, baryon acoustic oscillations (BAO) distance
parameter $\mathcal{A}$, and from the latest type Ia supernovae data, imposed
on cosmological models which allow sudden future singularities of pressure. We
show that due to their weakness such sudden singularities may happen in the
very near future and that at present they can mimic standard dark energy
models.
