  Type IIb supernovae (SNe) are important candidates to understand mechanisms
that drive the stripping of stripped-envelope (SE) supernova (SN) progenitors.
While binary interactions and their high incidence are generally cited to favor
them as Type IIb SN progenitors, this idea has not been tested using models
covering a broad parameter space. In this paper, we use non-rotating single-
and binary-star models at solar and low metallicities spanning a wide parameter
space in primary mass, mass ratio, orbital period, and mass transfer
efficiencies. We find that our single- and binary-star models contribute to
roughly equal, however small, numbers of Type IIb SNe at solar metallicity.
Binaries only dominate as progenitors at low metallicity. We also find that our
models can account for less than half the observationally inferred rate for
Type IIb SNe at solar metallicity, with computed rates ~<4% of core-collapse
(CC) SNe. On the other hand, our models can account for the rates currently
indicated by observations at low metallicity, with computed rates as high as
15% of CC SNe. However, this requires low mass transfer efficiencies (~<0.1) to
prevent most progenitors from entering contact. We suggest that the stellar
wind mass-loss rates at solar metallicity used in our models are too high.
Lower mass-loss rates would widen the parameter space for binary Type IIb SNe
at solar metallicity by allowing stars that initiate mass transfer earlier in
their evolution to reach CC without getting fully stripped.
