  We introduce the Parity-Odd Power (POP) spectra, a novel set of observables
for probing parity violation in cosmological $N$-point statistics. POP spectra
are derived from composite fields obtained by applying nonlinear
transformations, involving also gradients, curls, and filtering functions, to a
scalar field. This compresses the parity-odd trispectrum into a power spectrum.
These new statistics offer several advantages: they are computationally fast to
construct, estimating their covariance is less demanding compared to estimating
that of the full parity-odd trispectrum, and they are simple to model
theoretically. We measure the POP spectra on simulations of a scalar field with
a specific parity-odd trispectrum shape. We compare these measurements to
semi-analytic theoretical calculations and find agreement. We also explore
extensions and generalizations of these parity-odd observables.
