Quasiopenness seems to be generic to multi-field models of single-bubble open inflation .
Instead of producing infinite open universes , these models actually produce an ensemble of very large but finite inflating islands .
In this paper we study the possible constraints from CMB anisotropies on existing models of open inflation .
The effect of supercurvature anisotropies combined with the quasiopenness of the inflating regions make some models incompatible with observations , and severely reduces the parameter space of others .
Supernatural open inflation and the uncoupled two-field model seem to be ruled out due to these constraints for values of \Omega _ { 0 } \lesssim 0.98 .
Others , such as the open hybrid inflation model with suitable parameters for the slow roll potential can be made compatible with observations .