In this paper, the definition of the primer vector is extended to include nonoptimal as well as optimal trajectories. With this definition, simple tests are developed which determine how a given trajectory can be improved (in terms of velocity requirements). This problem arose in the study of the use of impulsive trajectories to generate approximate adjoint initial conditions for finite thrust vehicles. To do this, the optimum fixed-time impulsive trajectory must be found. However, since many mission analyses are done on an impulsive basis, a wider application is foreseen. Necessary conditions are developed for when an additional impulse can improve the trajectory; how interior impulses of a multi-impulse trajectory can be moved so as to decrease the cost; and when initial and/or final coasts improve the trajectory. In the case of transfers between circular, coplanar orbits a geometric interpretation is given. For the case of an inverse-square gravitational field, the components of the primer vector can be calculated analytically. Using Floquet theory, a convenient form of this solution is presented.