  Secondary eclipses and phase curves reveal information about the reflectivity
and heat distribution in exoplanet atmospheres. The phase curve is composed of
a combination of reflected, and thermally emitted light from the planet, and
for circular orbits the phase curve peaks during the secondary eclipse or at an
orbital phase of 0.5. Physical mechanisms have been discovered which shift the
phase curve maximum of tidally locked close in planets to the right, or left,
of the secondary eclipse. These mechanisms include cloud formations, and
atmospheric superrotation, both of which serve to shift the thermally bright
hot-spot, or highly reflective bright spot, of the atmosphere away from the
sub-stellar point. Here we present a methodology for optimizing observing
strategies for both secondary eclipses and phase curves with the goal of
maximizing the information gained about the planetary atmosphere while
minimizing the (assumed) continuous observation time. We show that we can
increase the duty cycle of observations aimed at the measurements of phase
curve characteristics (Amplitude, Phase offset) by up to $50\%$ for future
platforms such as CHEOPS and JWST. We apply this methodology to the test cases
of the Spitzer phase curve of 55-Cancri-e, which displays an eastward shift in
its phase curve maximum, as well as model-generated observations of an
ultra-short period planet observed with CHEOPS.
