We consider several factors concerning the design of observing strategies in cosmic microwave background (CMB) anisotropy experiments. First we consider the number of independent points on the sky one should observe given a fixed observing time. Given an assumed level of sky temperature fluctuations σ_sky_ and the presence of instrumental noise s in units of K s^1/2^ and a total observing time t_obs_ we find that there is an optimum number of points in the sky to maximize the confidence level of a detection. This number is a function of the signal to noise ratio R^2^ = σ_sky_^2^t_obs_/S^2^. We verify this analytical result with a Monte Carlo simulation, which also includes the correlation between different positions in the sky. Furthermore, using an n = l spectrum of Gaussian fluctuations, we show that arranging the observing patterns along a (great) circle, a raster scan, or a randomized pattern yields results which are indistinguishable in Monte Carlo simulations.