  Recent theoretical and observational studies both argue that the merging of
double carbon-oxygen white dwarfs (WDs) is responsible for at least some Type
Ia supernovae (SNe Ia). Previous (standard) studies of the anticipated SN
birthrate from this channel have assumed that the merger process is
conservative and that the primary criterion for explosion is that the merged
mass exceeds the Chandrasekhar mass. Han & Webbink (1999) demonstrated that
mass transfer and merger in close double WDs will in many cases be
non-conservative. Pakmor et al. (2011) further suggested that the merger
process should be violent in order to initiate an explosion. We have therefore
investigated how the SN Ia birthrate from the double-degenerate (DD) channel is
affected by these constraints. Using the binary-star population-synthesis
method, we have calculated the DD SN Ia birthrate under conservative and
non-conservative approximations, and including lower mass and mass-ratio limits
indicated by recent smoothed-particle-hydrodynamic calculations. The predicted
DD SN Ia rate is significantly reduced by all of these constraints. With
dynamical mass loss alone (violent merger) the birthrate is reduced to 56% of
the conservative rate. Requiring that the mass ratio $q>2/3$ further reduces
the birthrate to 18% that of the standard assumption. An upper limit of 0.0061
SNuM, or a Galactic rate of $4.6 \times 10^{-4}{\rm yr}^{-1}$, might be
realistic.
