  Experimental evidence for $I(J^P)=0(3^+)$ $\Delta\Delta$ dibaryon ${\cal
D}_{03}(2370)$ has been presented recently by the WASA-at-COSY Collaboration.
Here I review new hadronic-basis Faddeev calculations of $L=0$ nonstrange
pion-assisted $N\Delta$ and $\Delta\Delta$ dibaryon candidates. These
calculations are so far the only ones to reproduce the relatively small ${\cal
D}_{03}(2370)$ width of 70--80 MeV. Predictions are also given for the location
and width of ${\cal D}_{30}$, the $I(J^P)=3(0^+)$ exotic partner of ${\cal
D}_{03}(2370)$. Extensions to strangeness ${\cal S}=-1$ dibaryons are briefly
discussed.
