Abstract We present the power spectrum methodology used for the first-season COMAP analysis, and assess the quality of the current data set. The main results are derived through the Feed–Feed Pseudo-Cross-Spectrum (FPXS) method, which is a robust estimator with respect to both noise modeling errors and experimental systematics. We use effective transfer functions to take into account the effects of instrumental beam smoothing and various filter operations applied during the low-level data processing. The power spectra estimated in this way have allowed us to identify a systematic error associated with one of our two scanning strategies, believed to be due to residual ground or atmospheric contamination. We omit these data from our analysis and no longer use this scanning technique for observations. We present the power spectra from our first season of observing, and demonstrate that the uncertainties are integrating as expected for uncorrelated noise, with any residual systematics suppressed to a level below the noise. Using the FPXS method, and combining data on scales k = 0.051–0.62 Mpc⁻¹, we estimate P _CO(k) = −2. 7 ± 1.7 × 10⁴ μK² Mpc³, the first direct 3D constraint on the clustering component of the CO(1–0) power spectrum in the literature.