  Feedback control of quantum systems via continuous measurement involves
complex nonlinear dynamics. Except in very special cases, even for a single
qubit optimal feedback protocols are unknown. Not even do intuitive candidates
exist for choosing the measurement basis, which is the primary non-trivial
ingredient in the feedback control of a qubit. Here we present a series of
arguments that suggest a particular form for the optimal protocol for a broad
class of noise sources in the regime of good control. This regime is defined as
that in which the control is strong enough to keep the system close to the
desired state. With the assumption of this form the remaining parameters can be
determined via a numerical search. The result is a non-trivial feedback
protocol valid for all feedback strengths in the regime of good control. We
conjecture that this protocol is optimal to leading order in the small
parameters that define this regime. The protocol can be described relatively
simply, and as a notable feature contains a discontinuity as a function of the
feedback strength.
