In this presentation, we present scheduling algorithms that simultaneously support guaranteed starting times and favor jobs with system-desired traits. To achieve the first of these goals, our algorithms keep a profile with potential starting times for every unfinished job and never move these starting times later, just as in Conservative Backfilling. To achieve the second, they exploit previously unrecognized flexibility in the handling of holes opened in this profile when jobs finish early. We find that, with one choice of job selection function, our algorithms can consistently reduce average waiting time and average bounded slowdown relative to Conservative Backfilling while still providing a guaranteed start time to each job as it arrives. In fact, in most cases, the algorithms give better performance than the more aggressive EASY backfilling algorithm, which does not provide guaranteed start times. Alternately, with a different choice of job selection function, our algorithms can focus the benefit on the widest submitted jobs, the reason for the existence of parallel systems. In this case, these jobs experience significantly lower waiting times than Conservative Backfilling with minimal impact on other jobs.