Thermal fiber drawing is an efficient technique for producing optical fiber tapers whose operation regime gradually varies between multi-mode and single-mode. Here we present a comprehensive theoretical analysis of tapering optical fibers through changing their drawing speed on a standard fiber draw tower. We analytically calculate the drawing speed, drawing acceleration, and time needed to produce different kinds of fiber tapers and analyze the derived expressions to find the optimal fabrication parameters for the tapers. The obtained results inform how to most efficiently draw optical fiber tapers of different adiabatic shapes using the minimal pulling force for a given tapering ratio.