SIP (Systematics-Insensitive Periodograms) extends the generative model used to create traditional sine-fitting periodograms for finding the frequency of a sinusoid by including systematic trends based on a set of eigen light curves in the generative model in addition to using a sum of sine and cosine functions over a grid of frequencies, producing periodograms with vastly reduced systematic features. Acoustic oscillations in giant stars and measurement of stellar rotation periods can be recovered from the SIP periodograms without detrending. The code can also be applied to detection other periodic phenomena, including eclipsing binaries and short-period exoplanet candidates.