Results are compared for two integration methods used to solve the continuity, momentum, and energy equations of the steady-state solar wind. Method I is defined as that integration which starts at the 'singular critical point' and proceeds outward and then inward, and Method II is defined as that which starts at 'infinity' and proceeds inward. Both methods are used to obtain numerical solutions for the same three model equations of the solar wind. It is found that the results coincide within 1% for the domain where both methods provide exact physical solutions (out to a few AU heliocentric distance), but Method II is the only one which provides exact physical solutions over the entire interplanetary range. While both methods are shown to use comparable computer time for solutions within 1 to 2 AU heliocentric distance, Method II is recommended for solutions out to very large heliocentric distances.