  Non-linear redshift-space distortions ("fingers of God") are challenging to
model analytically, a fact that limits the applicability of perturbation theory
in redshift space as compared to real space. We show how this problem can be
mitigated using a new observable, $Q_0$, which can be easily estimated from the
redshift space clustering data and is approximately equal to the real space
power spectrum. The new statistic does not suffer from fingers of God and can
be accurately described with perturbation theory down to $k_{\rm max}\simeq
0.4~h~\text{Mpc}^{-1}$. It can be straightforwardly included in the likelihood
at negligible additional computational cost, and yields noticeable improvements
on cosmological parameters compared to standard power spectrum multipole
analyses. Using both simulations and observational data from the Baryon
Oscillation Spectroscopic Survey, we show that improvements vary from $10\%$ to
$100\%$ depending on the cosmological parameter considered, the galaxy sample
and the survey volume.
