This paper explores how the Tektronix Real-Time Spectrum Analyzer (RTSA) models can dramatically speed up searches for low-level spurious signals over wide frequency spans. In some cases the measurement speed can be improved by a factor on the order of 100. This speed improvement results from the much faster acquisition method used by a RTSA compared to a swept spectrum analyzer. A swept analyzer must measure the power in the resolution bandwidth (RBW) filter at each measurement frequency, which in general requires a time of a at least 1/RBW second. Then the swept analyzer must hop to the next measurement frequency, which is usually no more than half the RBW, and make the next measurement.