dynamics throughout the pre-explosion phase. Three-dimensional simulations of the same progenitor, with similar neutrino treatment, display episodic SASI activity, though a successful explosion is not yet obtained [@hanke2013]. @ott2012b evolved the same $27M_\odot$ progenitor with a more approximate neutrino prescription and a higher level of numerical perturbations, initially finding smaller SASI amplitudes than @mueller2012 and @hanke2013, though later confirming SASI activity (C. Ott 2013, private communication). The lack of the same level of numerical perturbations in the @mueller2012 models could mean that convection dominance instead of SASI dominance is dependent not only on the progenitor structure, but also on the details of the initial conditions.

It is the purpose of this paper to investigate some of these issues involving the interplay of SASI and convection, and the implications for successful explosions. In particular, we address the following questions: (1) Is there a fundamental difference between the transition to explosion in SASI- and convection-dominated models? (2) Can finite amplitude perturbations, generated in, e.g., multi-dimensional stellar progenitors (e.g., @arnett2011), tilt the balance in favor of convection in situations that would otherwise be SASI-dominated? (3) Does the SASI play any discernible role in convection-dominated systems? (4) Are there systematic trends in models close 