Accurate schedulability analysis of real-time programs, even in a language such as Real-Time Euclid, is NP-complete, essentially due to the exponential number of possible execution paths. Most of the exponential growth in the path space explored by the analysis is attributable to conditional statements in the programs. The paper presents two techniques using additional static information to improve significantly the cost of a typical schedulability analysis: the first detects non-executable paths by linking execution of conditional branches in different parts of the program; the second considers the branches of a single conditional, and eliminates paths by transforming conditional branches which cannot result in worst-case timing behavior. Each link or transformation can reduce the number of alternate paths the residual analysis has to consider by a factor of 2, thus allowing schedulability analysis to be practically applied to large real-time programs. An experimental evaluation of the techniques applied to both computer-generated and real programs indicates the value of this approach.